On early SLs the heater valve was shut with vacuum controlled by a switchover valve (vacuum relay so to speek), that was controlled by a microswitch at each heater lever. either side asking for heat opened the water valve.
Problems can be the valve, the vacuum, the switchover valve and the micro switches. Make the heater valve go closed or pinch off the flow to evaluate.
Bosch Master, ASE Master, L1
33 years MB technician