Hi!

The tapes played fine until yesterday when one
started to "warble" and slow down.

Uh-oh. How old is this tape deck? Since it ran into trouble with more
than one tape, it sounds like a bad drive belt is to blame. A bad belt
would also cause the constant "toggling" behavior you're seeing from
side A to B and back again.

Would a cleaning tape even play in there at his point?

A cleaning tape probably won't help now. You'll probably have to take
the deck apart and find all the bits of snarled tape. You'd be amazed
at all the places it can hide. Then, if you have any interest in
fixing the deck, you'll have to see how hard it will be to get at and
inspect the mechanism, especially the belts. Things like the rubber
pinch roller also need to be inspected.

This is much easier with some decks than it is with others. I don't
know exactly what unit you have, but something should be revealed when
you take both the top and bottom (if possible) covers off.

If and when you elect to do this, you should be careful. You will need
a good set of hand tools, including screwdrivers with small heads. A
needle-nose pliers could also be handy. Newer car tape decks have
motorized loading mechanisms and most of this stuff appears to be
driven by the main motor. As such, there will be timing relationships
between mechanisms that will have to be kept in mind. You should mark
all moving parts with something that won't come off so if they get
disturbed you can put them back.

I can't locate the tape head at this point. Looks like maybe
it pops up out of hiding after you put the cassette in.

That is how most car decks work...you put the tape in and the heads
are released. Sometimes simple spring pressure causes the heads to
contact the tape, and sometimes something more elaborate is used.

William