LawnDart and I were talking about this last practice in reference to some of the timer 'hacks' in the show. I took a close look at this pic and found the answer. Looks like they go with a big ol' round dial timer next to the HUD.
Old School Sweet
Tbirds Timers- Type and Location
Burner, you are right on with the cockpit timer. I have a picture here at home of Animal's ( Doug L.) cockpit and the timer is attached to the glareshield on the left side of the cockpit, just like your pic. FYI, all of the TB aircraft carry these although they are primarily used by the solos. However, maintenance will "switch" aircraft for various reasons. All they do is peel the number sticker off of the engine and put on whatever number they need. So the #2 AC might actually fly as #6 for a show or practice as needed. The last time I visited Animal at Nellis his airplane was used for a photo shoot with Miss Nevada and had the Boss's #1 on it but it was actually his plane. More worthless TB trivia from #7!