1998 BMW 323 dashboard lights

All of the bulbs for ilumination on the dash are only accessable from the backside of the instrument panel. That's unless you pull the the whole dash panel out but, you don't want to do that.
If you remove the under dash panels on both sides of the steering wheel you should be able to reach the sockets that hold the bulbs you want to change. The sockets are round and about the size of a nickel. They turn 1/4 turn counter clockwise to remove, and reinstall in reverse. Hope this helps, it's never an easy job.

Actually the instrument cluster is quite easy to remove, just the two Torx screws from the top of the cluster and the clock/display is popped out from under the clock, just put two fingers in under the clock and feel for the holes. The bulbs for the cluster and clock may have to be sourced from BMW.

If you take a bulb out, you should be able to match them in the aftermarket.