overheating. Not sure what the issue is

[kaysboat]

Yesterday the temperature light came on in =my 1980 C10, 250 straight six. I cranked the heater to max heat and did a bit of running around and stopped and started it before it had a chance to boil over. Each time I re-started it, the light came on after a few minutes of normal city driving.

This afternoon, I got out the shop manual and went to try to diagnose things.

1. The light came on as soon as I started the truck, even though it had been sitting for 24 hours.

2. I took the rad cap off and looked for water flowing through the rad with the engine running. Never seemed to flow even after a few minutes of running.

3. After it warmed up, I tried squeezing the upper rad hose. According to the shop manual, you should feel a surge of pressure if the water pump is working. I really didn't feel any surge.

4. I shut it down and felt the back side of the rad. It was hot in the upper corner of the driver's side, and cooler as I moved my had down the rad, and as I moved my had towards the passenger side.

I'm thinking my water pump may be pooched. However, before buying and replacing random parts, any thoughts?

Thanks.