haven't studied the wiring schematics too extensively on the zs, but I had an 88 stanza where the dash lights and tail-lights were on the same fuse. I somehow managed to blow the fuse installing a stereo and didn't realise they were connected. only way I found out was the nice cop that pulled me over and gave me a warning. I'd say check the fuses. might just be bad contacts.
Mine ('83 zxt) had same symptom with yours (sporadically going out). It became bad gradually and finally it didn't work at all.
I found that the terminal of the combo switch had been burnt and the plastic around it was melted down. Therefore the contact didn't work properly. I replaced the combo switch with an used part from '82 zxt and the problem went away. (New switch also has slightly burnt terminal though)
Try to confirm this. You need to take off a steering wheel in order to do this.
Hope this helps.