Spoilers
I think it makes sense. Gaeta had NFC who he was passing the information on to, as far as I understand it. So he gets on Galactica, and all that inside information is worthless. He doesn't know anything about the Resistance, because he's been providing information for all that time - sending information back would be a massive security risk. Anything he could say would most likely be disregarded as him simply trying to ingratiate himself with the Colonials, and turning coats once again. Again, the only person who could validate his information 100% was the chief - and Gaeta didn't actually know that he was providing info to the chief.
I haven't seen Exodus Pt2, so this may be inaccurate, but I think that's the whole point of why Gaeta didn't try to start bragging about himself being the informant...that, and it's just not his personality. He's also been used to masking his true allegiance for some four months, and spending plenty of time with Baltar...given that Baltar's entire claim to fame seems to be his ability to put on airs, I'm not surprised that Gaeta would try to differentiate himself from Baltar (unconsciously) by being his exact oppossite.