The seat post essentially serves as the butting on the top end of the seat tube. It is very common to damage the seat lug with a seat post that is too short; I have a 1950 Carlton Flyer with a wrinkle just below the seat lug which we believe is from a seatpost that was too short.
Since I don't think long seatposts are in the vintage era, A cheap and light campy-like seatpost is the Pazzaz 968 which is aluminum, and weighs an amazing 220 grams in the 400 mm length.
http://www.pazzaz.com/
This is a 2-bolt microadjusting post not terribly unlike Campagnolo, but with a super-record type of cradle, not with individual supports.
These long posts can also be used if for example the tube is splitting, to prevent additional force on the tear in the frame tube and in general to 'baby' a frame that was compromised at the seat lug.
It would be a shame to damage or ruin a vintage track bike only because you wanted to run a certain vintage seatpost. I'd say that 2.5" or 3" is the absolute bare minimum with most seatposts. I once lost a TREK 2300 frameset to a damaged seat lug (not from a short seatpost) and it was as if some thief stole the bike from me...
- Don Gillies
San Diego, CA, USA