I dont think that there is an absolutely satisfactory method of adding a se cond eyelet to a single eyelet drop-out..even from the outset of brazing it to the drop-out before the drop-out is brazed into the frame. Perfectly st rong joints can be obtained by careful preparation, but I have never found add-on eyelets that resemble those already forged into the drop-out. Perhap s they do exist in the States.
A perfectly round eyelet when brazed into place will only have point contac t with the edge of the drop-out, so it is better, I think to bite the bullet at the outset and file small flats on both the eyelet and the edge o f the drop-out, thereby creating line contact. Small chamfers on the edge s of the flats also increase the joint area, giving a larger brazed area.
This bike, short of proper repair, rechrome, repaint etc is never going to be spot on..so it's best to try to make as good a job as possible without e xpecting perfection. I would definitely silver solder this eyelet in place using a 40% silver rod ( like the one used for Reynolds 753 tubing) such as Easy-Flo No 2, with a melting point and fluid range of 608 -617 degrees .. I would prepare the eyelet with a flat and chamfer and having carefully filed off the original brazing material/silver solder ..I am assuming that it is stuck to the eyelet as this , being smaller,would have got hotter than the drop-out in the first operation.
Having cleaned the drop-out I would then deposit a sound layer of silver so lder on the drop-out. The I would deposit a layer of silver=solder on the eyelet. Having both surfaces well tinned with solder I would bring them bo th together, either by means of a small clamp or by wiring the joint with s ome nickel of stainless steel wire. Alternatively the eyelet could be held with a pair of jewellers or snipe-nosed pliers. The fluxed joint could then be reheated with as small a nozzle as possible, I would use a No1..that wo uld do the trick.
THis method would result in the chrome bluing in the immediate area of the joint. However, there are heat resistant pastes and putties that can be pai nted or stuck around the joint-area that would prevent the heat from disper sing into surrounding parts. Muggyweld.com has a product called Cool Blue H eat paste that appears to do this type of job.
The result should be an eyelet firmly fixed in two sound beds of silver sol der.
I have come across this type of breakage on several occasions, and found it also on frames on which the thin pressed steel gear cable chutes hav e been brazed on to the top of the bracket shell, as was the fashion in the 70s. In those cases the brazing material or silver solder had only adhered to the smaller, thinner and hotter component, the chutes, and not to the t hicker bottom bracket. If in doubt then put a deposit of rod on both surfac es and then bring them together....or play the flame on the bracket shell m ore than on the chute.
Better still don't use eyelets with only one eye when you know the project needs them with two ---they are available.
Not a perfect solution, but I hope it may help in some way.