Here's an explanation of how the locking mechanism for E3 and E9 works.
The problem I was having was actually with the E3 but they essentially work the same way. Below are pictures of both (E9 yellow, E3 green) in the locked and unlocked positions. In the unlocked position the lock turns the actuating arm to be in line with the latch, thus pushing it when the lock button is pushed in.
The actuating arm is secured to the core of the lock by a snap ring. In the picture below the top lock has no ring and shows the arm off the core. The bottom one, the pliers point to the snap ring. The large spring provides the return action when you press on the lock button.
What happened to my lock is that the actuating arm came off (shop installed with no snap ring; I could see residue of glue and I never found the ring inside the trunk) the lock therefore when I pushed the lock button, regardless of its position, locked or unlocked, it was unable to actuate the latch. It simply doesn't reach, it has no way of pushing on it. From this, I don't see how the solution of pushing repeatedly would do anything.
A second sloppy mistake by the shop was to not correctly install inner snap ring (you can see the ring clearly in the pictures above for the yellow car)) firmly in its groove so that by pushing hard enough the complete lock assembly was pushed into the trunk and I was able to push that against the latch.
I couldn't find a snap ring of the correct size to hold the actuating lever to the lock but McMaster sells a ring that did the job. It's trick to install but holds very securely. Since it protrudes a tiny bit more than the original ring, I had to very slightly grind down the inner teeth of the retaining disk. The whole assembly slides in and through the retaining ring when you push on the lock. The retaining ring has the lock code, BTW.
Lock with McMaster ring:
Now, I had a different problem on the coupe and it was that the lock would not easily turn back from the locked position into the unlocked position. In fact, sometimes it wouldn't turn at all and I'd have to try for a long time with uncertain results so practically speaking I couldn't lock the trunk. I figured the tumble pins might be gummy so I disassembled the lock to clean it.
The lock is a basic tumble mechanism with a shell (with bores and spring loaded pistons tha bear against the pins in the core) and a core:
The small pistons and springs get gummy in the shell and make turning of the key becomes unreliable or non-functional. I had tried lubricants with no benefit but perhaps a good bath of brake cleaner or acetone followed by graphite dry lubricant might have worked.
When you remove the core all the tiny pistons and springs will come out and it's impossible to place them back in from the inside so you have to pry open the small shiny rectangular plates on each side, place the core into the shell, place the pistons, springs and finally the plate and crimp it back in place. Sequence below:
