Tyler and Mike, you are both referring to BA9S bulbs, yet the Technical Manual
-- Which I trust implicitly
--
says BA7S. And it says the width of the bulb is 7mm. After a bit of poking around at various sources, it also seems to have "wings" on it rather than bayonets.
Since I happen to have my clock (partly) disassembled, I took my vernier caliper and measured the bulb. It's 9mm exactly wide by 20mm tall, plus or minus a half a millimeter because I didn't want to squeeze the glass too hard. And it fits snugly in the cavity in the clock. This bulb has printed on it: 12913 PHILIPS 12V 2W [squiggly line] K5614, which I had no problem finding on many web pages. Authentic Classics, for one, seems to have the incandescent version.
The bulb in Tyler's link is 3cm long, which is probably too long for the clock, don't you think? It looks like most BA9S bulbs are intended for sockets where you push the bulb in from the front and there's plenty of open space in front of the socket so it wouldn't matter how much wider than 9mm or longer than 20mm the glass would be.
The website
www.superbrightleds.com which has been mentioned in connection with the topic of LED bulbs, has BA9S listed, but most seem too long and too bright for our clock. Maybe this one?
www.superbrightleds.com/moreinfo/ba9s-ba7s/ba9s-led-bulb-1-led-ba9s-retrofit-car/3/