Intermittant starter failure, Work or break! Pick one! Options

[ammason]

So my 73 2.0L has an issue, but I can't track it down... 95% of the time it's great, but every once in a while, it just won't start. I have power - headlights, radio, etc; and if I push start it it starts up just fine, but 1 parking job out of 20 leaves me with nothing. No solenoid engaging, nothing but the dash lights coming on to let me know I have no oil pressure.

The five or six times this has happened I've been without a multimeter and have needed to get somewhere, so I've just pushed and gone, but it's damned annoying and one of these day's I'll get myself into a situation I can't get out of.

Yesterday I had to push start it in reverse in a parking lot while blocking up traffic. It's a helluva way to impress the chicks, let me tell you...

I'll do my best to test it when it happens next, but am I describing typical symptoms of a part needing to be replaced? Ignition switch? Solenoid? Bueller?

Thanks!

Aaron