Can someone tell me what this part is on my 98 chevy c1500 ?

[unknown2343]

Does the radiator have the small hose at the neck that returns to the reservoir bottle?

Yes it does. It’s hooked up

 

[movietvet]

Use a small worm gear hose clamp and install close to the radiator spout, that the hose slips on, put the clamp on about 1/4" to 1/2" from that spout end and tighten the clamp down slightly but not all the way, that would close it off completely. Then run the engine to operating temp, drive it, and monitor the temp.