A lot of times it's the optocoupler that is the culprit in an original Fender. The heatshrink tends to crumble and allow light to leak in. If it's really bright it is probably bad and leaking light, but you should see it flashing a little bit.
You do know that you have to have the footswitch or need to short the jack on the back of the amp for the tremolo to work, right?
If you look through the external speaker jack (or the second input jack) when the tremolo is on can see the flashing from the coupler?
I would highly recommend emailing Jon at Tonecraft Amp Repair. He makes the absolute best replacement, the Surf Bug, for these and he'll tell you how to troubleshoot the problem. He also won't try to sell you a Surf Bug unless you need it. I've used these twice and they are much better than most replacements.
If you email him you won't get a reply until evening in Texas after he has closed up shop, but he'll help you out.
http://www.tonecraftamprepair.com/html/surf_bug.html