Heater Core

I think you are talking about the small overflow hose near the radiator cap on your 1992 GMC 1500 Pickup, That is the only low pressure hose in your cooling system. If your radiator is copper the pipe can probably be repaired by you local radiator shop. If the broken pipe is plastic your best bet may be to replace the radiator. Sometimes it is possible to replace the plastic tanks but that does not always work out well.