I assume its a type of snare drum? Maybe? Custom made or were these sold back in the 60’s? Kind of looks like a metal trash can lid on a stand. 
its seen early in this performance. Paul Wheatbread shows off a bit twirling the drum sticks. A great band screwed up by breaking up with their producer.
https://youtu.be/1hyJDLyUAoc
Jerry Fuller produced their biggest hits. The band’s popularity sank after breaking up with Fuller. That partnership might have churned out another dozen great hits.
Wow. That wasn’t even CLOSE to answering the OP’s question.
I got burned by the edit time out and had to reply to my own OP. Wanted to finish explaining why such a great band only had 4 big hits.
Always wondered about the thing the drummer is banging on.
I suspect it’s not an instrument at all, but rather just a prop. The guy is making motions as if he’s playing a regular drum kit. He seems to be, basically, “air-drumming”. It goes along with Puckett not singing into a microphone and the guitarists not having their instruments plugged in.
The drummer uses an actual kit in other performances:
I thought Puckett was singing into a boom mike (out of the frame) above his head.
<shrug> I didn’t think about them faking the performance. Guess that possible. That would explain why Paul Wheatbread had time to screw around twirling the drum sticks.
A little off topic, but I recently realized that the Gary Puckett songs not only recycle melodies, but can be arranged to form a story.
Young Girl - she wants to, he doesn’t.
Lady Willpower - he changes his mind and convinces her to do so, too.
This Girl is a Women Now - success!
Woman - “Have You got cheating on your mind?” She’s looking to end it.
Over You - She ended it.
I’m pretty sure he is “playing” a table. They are lip syncing to the record anyway. Maybe there were issues with setting up a drum kit for the shoot.
Yes it’s a table. Fascinating in retrospect how it was considered no big deal to not even make that much of an effort to fake a real performance.
American Bandstand typically had the bands lip sync. I think there were a few exceptions.
Anyone know if Midnight Special and Don Kirshner’s Rock Concert used live band performances? I always thought they did, but we were watching it from live tv, off rabbit ears. No replay or pause buttons. 
Video isn’t the best. I was trying hard to see something there. Some kind of metal surface or a tightly stretched hide. You have sharper eyes than me to see for sure that it was just a table top.
Never occurred to me they faked it back then. Interesting to learn they did.
Oh yeah. Maybe on Ed Sullivan, Hollywood Palace, and Smothers Brothers, groups actually played their songs, but on Hullabaloo, American Bandstand, The Monkees, Partridge Family, and shows of that ilk, they generally lip synced to their records. The lack of microphones and guitar chords was a dead giveaway. And brass and strings from a 4 piece rock band.
In that Union Gap video, I think that was just a spare bass drum or floor tom head he was pretending to play.