Ive usually had bad capacitors in sound section cause this.

I had an EATPM that did this very thing. What I found was a bad connection with the EPROM and the socket. I ended up just tweaking the pins on the chip and it solved it.

Let's see a picture of the board.

That's always the easiest thing to try. Carefully reseat all of the sound roms, and the cable connections. What happens when you run the sound test in diagnostic mode? Did you try adjusting the Volume pot in the cabinet? Try cleaning it with contact cleaner?

i had no speech on my earthshaker recently, reseating the x2 cpu chips on the cpu boards fixed the issue.

I agree with pinball plus, top left corner of mpu, replace the capacitors. Fixed many system 11 games.

From the looks of your board, there looks like battery acid repairs were done in the area around J21, where the ribbon cable between the boards connects to the MPU. The music test is intended to test the sound card, but in order to do it properly, it has to be able to communicate through U42 on the MPU board to J21. The video you posted of your sound test, I am pretty sure you are not just missing the one sound, I believe it is playing the wrong sounds in a couple of those tests at well. Perhaps someone who owns a Taxi can confirm which sounds are incorrect.

Regardless, from the pictures you posted, it appears that SRC3 has been replaced. It lies along the communication lines that runs between U42 on the MPU board and J21. If you have a break in one of these lines, your sound board will do funny things like play the incorrect sounds during the music test. You may want to check the continuity on all the traces I have circled in red.
U42 (resized).JPG

edit: You may want to also check all of the connections from J21. The rest pass through SRC1, and there are a couple that come from U41.

verify continuance between the 8 data lines coming for the 6821 @ U42 (pins 10-17) and the pins 3-10 on the ribbon cable connector, sounds like you are missing at least one, you could test with a logic probe during operation to make sure all 8 lines actually get pulled low when activated but the continuance test is easier and quicker

you may find you need to add another jumper or two if any lines fail

I don't think that bubbling is corrosion related. Ive seen a lot of older circuit boards do that. I don't believe it will affect the boards operation.

Edit: I assume you are talking about the bubbling in the green finish over the trace lines.

That is glue to hold the jumpers in place. Not very pretty but it's effective.

I have to agree with GRUMPY on this one, I am pretty sure that is just glue.

Typically corrosion builds up on the battery side of the board. That glue looks like it was placed there after the repairs were made.

not unusual to find breaks cause by corrosion under the resistor networks - tough to see but easy to find

i use clear nail polish to secure the kynar wires used for repairing so the glue is fine or whatever that is