I have recently bought a German edition 1977 450SL

Everything was fine until I took it on a 4 hour trip.
A few hours after arriving, I went to start it and the battery was dead.
Boosted it.
Checked voltage and it was 13.9V so charging OK
Did several short trip, everything was fine.
Next day did 4 hour trip home.
A few minutes after arriving it would not start. Battery dead.
Boosted it.
Voltage was 11.6v so not charging.
Charged battery a bit and a few hours later started fine 13.8V - charging OK again. Everything fine since on short trips

Seems like it won't charge when thoroughly HOT?

Battery is old but cranks fine normally
I get a red battery dash light when I turn key on which goes out after started.
Did not get a red dash light during long trip ( at least didn't notice one?)
Belts are old but good and tight
Trips were daytime not using lights, AC or anything

Any ideas?

Does it have an external voltage regulator or jut the one on the back of the alternator ?

This will be to diagnose because it normally is working fine.

I will change the belt and battery, but don't see how that will change things?

Thanks for any help
Bill Crick