Hey, I just did myne too. As you say, a pain. Thought i'd chuck up a description of what i did just incase it helps others using the search..
The bulb is a H6W or 68161 in NARVA brand. Halogen Bayonet with offset pins. NZ$15 trade or NZ$22 retail.
To replace a side light bulb in a 156:
-The bulb is in the centre of the headlight.
-Behind the centre of the headlight there is an adjuster thing with a hex rod sticking up - don't touch that!
-Instead access to the side light is gained through the inboard twist cap, about 80mm diam with grip around it and a single tang at the top. In all cases they turn anticlockwise 20° or so and then pop off. There are two of these caps on each headlight. One of myne was extrmely tight to turn so i used a spider style filter wrench. Once off i shaved the selaing ring a bit so it wasn't as fat and wasn't so tight.
-Once the cap is off look for a black plastic wing/ tab. This is difficult to see on the non timing side end so i recommend taking the equivalent cap off at the timing side (drivers, RHS) just to see what you are dealing with.
-The Black tab should be oriented vertical (above the pivot which is the light socket).
-With finger or very carefully with a tiny flathead screw driver release it from vertical and then turn this inboard (mirrored depending on which side of car you are on) Ensure you are rotating it about the pivot described, not rotating about itself otherwise you'll break it. (perhaps described as a turn not a twist)
- It will turn up to 120° but only needs to turn 90° (this can be sen by watching the bulb turn from in front of the headlight)
- When at 90° apply some pull rearwards (by hand so you get a proper feel of it) It will wiggle a bit but will slide rearwards eventually, It's a wobbly push fit.
- Bulb is a halogen bayonet type so push down, twist to replace and pull out. The bulb is a H6W or 68161 in NARVA brand.
- When replacing the bulb don't touch the glass. Wear a new latex glove or just use a tissue or something.
- Replacement is reversal of above, however i found it the tab doesn't lock back at vertical as well as it did originally.
I fully don't recommend using a set of pliers to do it as until you have done it once, you are likely to twist the tab and break it.
Let me know if this was useful. Also let me know if i confused you or if any other info would be useful. I am considering putting a tidier version into the how to thread