In the final two months of Vincent van Gogh’s life, he mentions one particular woman’s name in separate letters to his brother Theo, and to his mother Anna and sister Willemien. All the letters are sent from Auvers-sur-Oise, a small hamlet on the banks of the river Oise, and the town where Van Gogh died on 29 July, 1890.

The first mention is this one from Vincent to Theo, post on 24 June, 1890, a Tuesday and just one month and one week prior to his death:
I hope to do Miss Gachet’s portrait next week, and perhaps I’ll also have a country girl to pose too.
Four days later on June 28 June – a Saturday –  having not heard back from his brother, Vincent writes him another letter, this time writing at length about “Miss Gachet”:
Yesterday and the day before yesterday I painted Miss Gachet’s portrait, which you’ll see soon, I hope. The dress is pink. The wall in the background green with orange spots, the carpet red with green spots, the piano dark violet. It’s 1 metre high and 50 wide. It’s a figure I enjoyed painting – but it’s difficult.
Despite Van Gogh’s stated “enjoyment” of the painting, he admits to having some “difficulty”, but doesn’t say whether this is due to the reticence or reluctance of his 20-year subject, or for other reasons.

Whatever the issues, Van Gogh assures his brother he will “have another go” at painting the young woman’s portrait. Her father – Dr. Gachet – has given the artist his permission.
He’s promised to get her to pose for me another time with a little organ. I’ll do one for you – I noticed that this canvas looks very good with another horizontal one of wheatfields, thus – one canvas being vertical and pink, the other pale green and green-yellow, complementing the pink.
And then Van Gogh – still in the same letter – waxes lyrical about the female form, the colors of dresses and the romance between “art and nature”:
But we’re still a long way from people understanding the curious relationships that exist between one piece of nature and another, which however explain and bring each other out. But a few, though, do feel it, and that’s already something. And then this has been gained, that in women’s clothes one sees very pretty arrangements of bright colours. If only one could have the individuals one sees pass by to do their portraits, it would be as pretty as any past era, and I even think that often in nature there is currently all the grace of Puvis’s painting, between art and nature.
When Theo responds to Vincent two days later, in a letter sent from Paris [less than an hour by train to Auvers] on 30 June,1890, he alludes to their new baby falling ill, thus preventing the family from coming to see him in the country. Theo flatters his brother, saying of a portrait he hasn’t yet seen:
Your portrait of Miss Gachet must be admirable, and I’ll be pleased to see it, oh those little patches of orange in the background…
Skipping back to 5 June, Vincent in a letter to his mother Anna, makes an allusion to the young Gachet girl as well, along with a medical diagnosis of his brother’s failing health [Theo would be dead within six months of Vincent’s death]:
The doctor here has been very kind to me; I can go to his home as often as I like, and he’s very well informed about what’s going on among painters these days. He’s very nervous himself; most probably that hasn’t improved since his wife’s death. He has two children, a girl of 19 and a boy of 16. He tells me that in my case working is still the best way to keep on top of it.  Well, in the last fortnight or 3 weeks that I was in St-Rémy I worked from early in the morning until the evening without stopping. And only stayed in Paris for a few days, and got started again straightaway here.
Theo was waiting for me at the station, and my first impression was that he looked paler than when I left. But talking to him and seeing how he was at home, I was encouraged — although he was coughing — but it really is true that he has not got worse during that time. So even if it were to remain the same, I would almost dare believe that this might already be counted as something gained. And next year he’ll get stronger rather than weaker. It’s a matter of patience, his constitution and the circumstances of his life…
This sounds like a son trying to assure his mother not to worry, or interfere, and more specifically trying to reassure his mother that her eldest son is working hard and paying his way, even if he doesn’t have a real job and isn’t earning any money.
On the same day, 5 June, Vincent writes to his sister Willemien:
For me the journey and the rest up to now have gone well, and coming back to the north distracts me a lot. Then I’ve found in Dr Gachet a ready-made friend and something like a new brother would be – so much do we resemble each other physically, and morally too. He’s very nervous and very bizarre himself, and has rendered much friendship and many services to the artists of the new school, as much as was in his power. I did his portrait the other day and am also going to paint that of his daughter, who is 19. He lost his wife a few years ago, which has greatly contributed to breaking him. We were friends, so to speak, immediately, and I’ll go and spend one or two days a week at his house working in his garden, of which I’ve already painted two studies, one with plants from the south, aloes, cypresses, marigolds,5 the other with white roses, vines and a figure.
“The figure” in the garden, of course, was young Marguerite Gachet.

And so one rather has the impression of the lonely artist welcomed into the Gachet home after a traumatic year in the unfriendly confines of the nuthouse in St. Remy, and in these cozy, safe, pleasant surroundings he comes across a shy, unmarried young woman surrounded by the vivid curtains and colors of the French summer – in full bloom.
Since her mother is deceased, and her father is a busy doctor, one can rather imagine the 30-something painter regularly brushing shoulders with the much younger Marguerite, as he goes about his painterly ways.

But what did her father, Dr Gachet, make of Vincent’s interest in his daughter? To paint, of course.

Some, such as the author Derek Fell have speculated that in the painting Marguerite Gachet in the Garden, Marguerite is dressed in white, “like a bride.” The garden is filled with white roses and light lemon marigolds. Fell speculates on rumors swilling in Auvers at the time that Van Gogh considered Marguerite a friend and that she desired a relationship with him.
Fell goes on to state in his book Van Gogh’s Women:
Dr. Gachet, though, had not given permission for the sittings and when he learned of the two sittings in two consecutive nights he was quite apprehensive about any relationship they might share. Dr. Gachet asked Van Gogh to end his relationship with 21-year-old Marguerite…
On 22 July, after an unusual silence from Vincent, Theo writes a letter to his brother suggesting he go to Dr. Gachet.
…I hope, my dear Vincent, that your health is good, and as you said that you’re writing with difficulty and don’t speak to me about your work, I’m a little afraid that there’s something that’s bothering you or that isn’t going right. In that case, do go and see Dr Gachet, he’ll perhaps give you something that will buck you up again. Give me news of you as soon as possible.

On 14 July, in one of his last letters, Vincent writes another short letter to his mother:
But precisely for one’s health, as you say — it’s very necessary to work in the garden and to see the flowers growing.
For my part, I’m wholly absorbed in the vast expanse of wheatfields against the hills, large as a sea, delicate yellow, delicate pale green, delicate purple of a ploughed and weeded piece of land, regularly speckled with the green of flowering potato plants, all under a sky with delicate blue, white, pink, violet tones.
I’m wholly in a mood of almost too much calm, in a mood to paint that.
He sounds like he may be in love with those delicate colors and white, pink, violet tones after all, doesn’t he?

More: The Sad Story Of Vincent Van Gogh And His Lovers – dailyartmagazine