'87 4kcsq - trouble starting.

[James Hanson]

When I tried to start my car today, it didn't...
turn the key to on, everything seems normal, turn it to start, and
everything shuts off.
I can hear the solenoid kick over.

Wait a bit, and all the electrics come back on.  Try to start it,
everything shuts off.

Repeat.

Disconnected the battery, let it sit a while, reconnected it, and it
started fine.  This has happened a couple times now.  The first few I
counted as anomalies, but today it made me late.  That counts as a problem.

Any ideas what the problem might be?

Thanks,
Jim