At a seemingly unrelated time later my mobile Gmail on my Nokia 6233 failed to connect with the (misleading) error message
"This program requires a working data connection... Please check you signal stength."- whilst the GPRS/data indicator is active and all other apps work.
I did not get the correlation to the https setting, but a couple of days later (yesterday) it struck me... and it turned it off again ... voila, gmail mobile wors again.
(and turned it on again -> fail ,turned it of -> works).
Turns out, that this is well documented:
Some products that connect to Gmail, like Google Toolbar, are not yet compatible with https. We're working to identify issues like this and get them fixed, so visit your product's Help Center if you encounter problems after enabling this setting. In particular, check out this Gmail Help Center page if you use the Gmail mobile app, as you may initially hit an error when you try to use it (we're working on a fix).
(from the gmail blog)
Bad thing is, my 6233 is running with gmail v1.1.1 and there does not seem to be an update for it...