Lots of info in this listing for a watch very similar to yours, same case, different dial configuration. Oddly, the seller is US-based and I can find his other listings in English/USD, but this one only comes up in Spanish. The description is English so still useful I hope.
https://www.ebay.com/itm/Reloj-de-pulsera-Vacheron-Constantin-Rectangular-con-asas-de-lagrima-grande-de-fantasia-de-multiples-/143200488076?_ul=NI&nma=true&si=Y4kycBOOBLmhS7ewRVNo2Bxd%2FBw%3D&orig_cvip=true&nordt=true&rt=nc&_trksid=p2047675.l2557
For posterity:
"For sale is a Vacheron Constantin yellow gold rectangular manual-wind men’s wrist watch with
large fancy fluted lugs, also known as
multi-teardrop lugs. The watch is
triple-signed on its dial, case, and movement.
The watch has a two-piece rectangular body made of 18k yellow gold with a snap-on case back and fancy
multi-teardrop fluted lugs. The case measures 21mm wide (without crown or lugs), but measures about 25mm wide inclusive of the lugs. The case measures 27mm long without the lugs, but measures about 40mm long inclusive of the lugs - which makes the watch appear far larger than the case alone measurements would otherwise indicate. The watch is about 7mm thick (including the crystal) and has an original crown. The outside of the case is stamped twice with the queen’s head Swiss proof mark (on the side of the case and one lug).
It has a two-tone silver dial signed “Vacheron & Constantin Geneve” and “Swiss” with applied yellow gold button and Roman numeral indexes, a black painted chapter ring with black outer minute division indexes, yellow gold baton hands, and a subsidiary seconds dial with outer five second division indexes. The inner section of the dial is in excellent condition, while the outer section of the dial and the subsidiary seconds dial is in good condition showing more age as you advance towards the edges of the dial. Please refer to the photographs of the dial.
The case number is 285920 and the movement number is 435999. The watch was likely manufactured in the late 1930’s. The caliber 435/3C tonneau movement has “fausses cotes” decoration and is signed “Vacheron & Constantin Geneve Swiss” and marked 435999, “Adj. To Temp.,” and “Seventeen 17 Jewels.” On the inside of the case cover, which also features “fausses cotes” decoration, is marked “Vacheron & Constantin Swiss,” 285920, with several proof marks, including “18K,” “0.750,” a queen’s head Swiss proof mark, and key.
The back of the case is engraved “Gustav Goob,” who was born in Germany in 1881 and became a well-known brew master in the United States. So, you get a little bit of history with the purchase of the watch. The engraving is very well done and, unlike poorly done engravings, does not detract from the beauty of the watch.
This exact model (Movement No. 431665, Case No. 285939) sold at Antiquorum on November 13, 1994 (lot 236) for 9,200 CHF (about $ 6,900 back then). Another one sold at Christie’s on November 11, 2013 (lot 94) for 5,000 CHF (about $ 5,440). Another one (Movement No. 442130, Case No. 298668), in pink gold, was offered at Antiquorum (lot 156) on October 24, 2004 with an estimate of 9,500 - 11,500 CHF (about $ 7,850 - $ 9,500 back then).
The watch comes with a new reddish brown leather strap with an aftermarket gold-tone buckle. No original box or papers. The watch was recently serviced and is in proper working order and keeps approximate time, but it is sold in “as is” condition with no warranty because it is a vintage wrist watch. I will be listing other Patek Philippe and other fine quality watches for sale in the future. Please see my feedback as a seller of high-quality vintage watches."