On my 1978 300CD, the battery and both brake lights keep coming on at an idle. I have had the alternator checked, and they say it is OK. Any ideas?

 

Consider a new battery, after a load check of the battery and asking whomever checked the alternator to verify the alternator's idle output voltage is within in spec's, especially with a electrical load. Could be the brake light switch, but those years did not have the switch problems common in the late 80s/90s models.