The real check would be to take it off and hold it up to sunlight. If you think it's cracked, then in all likelihood it is! They are notorious for cracking the driver's side, but certainly do also crack the passenger side too. One simple thing you could also try, just to eliminate doubt, is to check/tighten the two bolts that connect the crossover pipe to the header flange. I've had them loosen up over time, and create a leak at the flange. If that doesn't work, then try the "hose stethoscope". After that, prepare to take the thing off and get it welded, as I suspect you'll need to do.
It's really a shame that GM did not have the foresight to have the exhaust manifolds for TR's made from stainless steel originally, as they did for the TTA's in 1989. This would eliminate this reoccuring problem...