I would be connecting the center tap (yellow and white) to my +12V and grounding the remaining wires with NPN transistors. I want to use a wave drive sequence:

0001
0010
0100
1000

I just don't know which wire is what!

I think this is equivalent:

BLK
BLU
GRN
RED

I thought I had it figured but it's not working. I'm trying to troubleshoot if it's my circuit or my step sequence.

Try black/red/green/blue and if that goes the wrong way reverse the sequence. If A and B are the windings you want something like
A+, B+, A-, B- as the sequence.

Well you can use a multimeter to determine if your motor is wired up as per the diagram. Stepping is always A+/B+/A-/B- (or the reverse order) Its arbitrary which end of a winding you call + or - BTW - if the motor turns the wrong way either reverse the sequence or swap +/- on one winding only.

Its arbitrary which end of a winding you call + or -

If it's arbitrary which end of a winding you call + or - then you are saying that any step sequence will work, as long as you alternate between coils, and switch polarity every time a coil is addressed. In other words, label the wires An and Am and Bn and Bm, then any sequence AnBnAmBm or AnBmAmBn or AmBmAnBn will work?

Yes, you just need to go round the circle in one direction of the other and not double-back or jump two steps in one go.

There are 24 permutations possible for 4 wires, but since its only the cyclic order that matters divide that by 4 to give 6 possibilities. 4 of those possibilities look like AABB and 2 look like ABAB, the latter two case are the ones you want. You have 1/3 chance of getting a viable wiring at random in fact!

The problem is exactly that of visiting the 4 corners of a square once only. Correct solutions don't cross a diagonal.

No I don't think anyone does. I have found I have to swap the wires round (or the sequence) until I get it right. After that the same colours from the same sort of motors are consistent.