The original run of the Gibson Thunderbird had been 1963-65 and then 1966-69, the latter period with the "non-reverse" body style. It was brought back for the Bicentennial with new pickups and a new, three-point bridge. Even though the bass that Gene used didn't have any Thunderbird logo on the pickguard everything else about the bass suggests it was a 1976 or '77. The Thunderbird had the same suffix logic as the Firebird so the IV simply meant that it had two pickups. It replaced the Dan Armstrong as the backup bass in the latter half of July 1977.
Apart from the replacement pickguard there were a few other modifications to the bass. Most obvious was that the "neck" pickup had been replaced by a DiMarzio Model One. You can compare the photo below to this 1976 Gibson Thunderbird. Much like Spector no 1 and the Dan Armstrong, this bass had gotten the Schaffer-Vega wireless transmitter built into the bass. It only made it on stage once during the CanAm Tour but as you can see, when it did it did not sport any cable.
The Thunderbird was retained as the backup for the next tour in support of Alive II. It had gotten a new mirror pickguard but otherwise seemed to look exactly the same. It rarely saw any action but as bootleg video fans know it was called upon in Largo in December (see also below).
As far as we know, the Thunderbird only made it on stage once during this tour (as seen above). It was still at the ready on Gene's side of the stage throughout January but once the Spector no. 2 joined the ranks there was little chance that the Thunderbird would be called upon.
Based on the photos currently available to me it doesn't appear that the Thunderbird made the trip to Japan in March and April but I assume that it did. It wouldn't have made much sense to travel with only one backup (Spector no. 2 can be seen backstage in Japan). The coup de grace for the Thunderbird was also its most high-profile appearance. During the on-stage fight scene in KISS Meets the Phantom we see Gene and his evil KISS clone grapple over the Thunderbird.