Thoughts about your issue.
1) Don't asssume (You know the saying), test and conclude. Borrow or buy a decent video scope, they are $100-150 for a decent one. (Less used on Offer up or CL.) Then you can see in the tight spaces.
2) I agree with a couple others, you likely when taking off or loosening the upper radiator hose at the thermostat housing caused the hose, housing, or housing to block gasket to give up the ghost and leak. The housing to block gasket area is hard to see with the alt in place. So take your time and get a close look. The silver linning in this is it leaks when running, VS only when driving or very hot. That housing is about 10" long if you have not removed it before.
3) It could be coincedental you found somehting that was leaking prior. So look closely at the freeze plugs, block heater (If yours is on the passenger side.), head gasket, and head for a crack. But keep in mind that head to block gap/line could be just the path the leak is traveling down then dropping mid engine but coming from something simple.
4) How I always try to determine a leak is to look at the coolant overflow tank and then open the radiator. (When cool) to see if the coolant is down. Then you can conclude a coolant leak. (You mentioned you are not 100% sure.)
5) As stated above add coolant dye and do some testing.
a) Do you see water or dye in the oil. (Milky white on oil cap or on dipstick. If so head gasket, water pump bolts, or oil cooler seals. May be a seperate issue, don't assume.)
b) Do you get instant pressure build up in the radiator with your hand over the radiator opening when the truck is running? (Do it when cool, don't burn yourself on 200 degree coolant.) This points to a head gasket, so pick up a test kit and test for gases at the radiator cap hole to confirm. Yes on gasses, then clearly head gasket.
c) Do a radiator pressure test. (Autoparts store will likely loan or rent you one.) Start at 10psi and see if you can find the leak. If not go to 13psi. Go to zero PSI and start the truck if pressure builds again points to a head gasked. But I would not go higher than 13psi as these engines are all aging. You can make it leak, but without the engine running or getting hotter. Now with the die and flashlight you can see where the leak originates from. Remove what is needed if you cannot see the start of the leak and find where it is coming from. (IE could be the thermostat housing (But you cannot see that area with the alt in place, but running along the block, to the head, down the head gasket, and dripping mid engine.)
Wishing all the best and that it is something simple!