1970 50HP dies at low speeds

[MD-Mercury]

I am restoring my grandfather's 1970 Starcraft with the 50 HP Mercury motor. Both times I have had the boat out, the motor starts easily and runs at a no-wake speed for about 5 minutes before opening it up. She runs great at the upper end of the throttle for as long as I want to run it there. Then when I back it down to either a stop or slow cruise, she shuts off. Restarting is iffy, but seems to idle fine in neutral. If I tried to engage the prop, she cuts off. As if she isn't getting enough fuel. I have been successful getting her back up to full speed if I have someone hand pump the primer ball while engaging the throttle. So while that does seem to be a fuel supply issue, I have heard that it may be the coil breaking down at low speeds when it gets hot. Does anyone know with certainty what the problem may be? Serial number on the motor is 2862093.

Thank you

 

[DeepCMark58A]

Order a fuel pump rebuild kit, they are cheap enough and easy to do. Also adjust the low speed idle screw on the carb.