Both my Vintage Spyders(I had a 2002, now a 2016) have a U-1 garden tractor battery. However, they are usually all the way in the rear behind the engine and transmission, but on the driver side(same side as the starter). The starter is right there so battery cables are 2 feet or so each.
I have a 400 plus CCA garden battery from Tractor Supply, it's been good for 5 years so far. It weighs less than twenty pounds. It's a standard lead/acid wet cell battery.
@The Lost Spyder is the battery inside the passenger compartment or is it in the engine compartment tight to the firewall?
As Robert says, the size should be on it somewhere and/or the CCA or amp/hour rating. To duplicate what you have, measure it carefully and search online for the size. It is likely that it may be a motorcycle battery size, or possibly a race car size.