Not exactly "vintage" but it's possible to ride on the track. With two 24" and two 26" road bikes, my kids have some nice tools to ride on in future. But I thought that it would be a nice challange to convert one 26" into a real track bike. The frame has horizontal dropouts, so it's possible to tension the chain. For a geared bike you need a certain minimum chain stay length, so the clearances are not as tight as you would expect from a nice road or track bike. Anyway, with the correct components, it will make a very nice track bike.
Frame and fork: Giant TCR 26" alu 6061 frame, fork with carbon fork blades, alu steerer tube
Cranks: Miche Young 155mm cranks, 44T
BB set: Miche BC
Front hub: Shimano Dura Ace 28H HB-7400
Rear hub: Shimano Dura Ace 28H HA-300 (I think)
Rims: Mavic GL330 S.S.C. 94 28H tubular
Tubulars: Vittoria Competition Juniores 21-26" (and some expensive Vittoria and Conti Time Trial and track tubulars)
Sprocket: 19T 1/8" (others available)
Chain: KMC Z410 silver coloured 1/8"
Pedals: Shimano Dura Ace PD-7401
Saddle: Selle San Marco Concor Junior Light
Seat post: Zoom I think).
Stem: Truvativ Holzfeller 40mm. Have a Look Ergostem available, but hard to set up nicely and short extension. Maybe can use it later.
Handlebars: Zoom Buckup 37cm c-t-c, drop 145-ish mm
Bar tape: Cork white
To be done:
Cut internal thread into front axle and fix with bolts and flat washers
Cut steerer to length (will wait until bike will be ridden)
Add chain tugs
Find out correct gear ratio and adjust chain length. Now it's 1/2 link too short. Sprockets available, may have to buy extra chain ring.