I recently opened an Ameritrade account only to find they
automatically exercise call options at expiration.  I'm looking for a
broker (preferably online, but any will do) who allows options to
expire.  I want to make a $400 call option purchase without having
$24,000 in my account to back it up.  Thanks!

That sounds very odd to me.

I do not know a great deal about Share options, but I used to know
quite a lot about Currency options - specifically the Philidelphia
Traded Options market.

I doubt the rules are that much different.

With those the only time you had to 'fund' them (eg: put up a
statutory goodwill deposit - joke intended) was when you were
'writing' (selling) the options.

When buying options it was IIRC usual to just get paid the difference
if they expired while 'in the money'
Automatic exercize and 'taking delivery' sounds plain weird to me.
Especially as, with shares, they might be in the money, but not by
enough to cover sale transaction costs.
This sounds puzzling