no spark - '91 500SL

Guys & Gals,
Of late, our 500SL has had interrmittant starting problems (no spark), and episodes of the alarm sounding for no apparent reason! More specifically, sometimes it will start, and sometimes it will not, she turns over fine. Using a spark tester, have determined lack of spark, but then she'll start! And also, the alarm has started 'beeping' for no apparent reason.
Some recent history, if this will perhaps help. Over the winter, I replaced the alternator and the battery, and did a complete brake job. First time out of the garage, she drove fine for a couple of days, then she stranded the wife (not good) at the local CVS. When I tried to start her, plenty of cranking, no start. After about 20 minutes, and just before a friend was about to tow her, she started! Similar circumstances have occurred at least three times!
Any thoughts?

Gene