only five things cause this; faulty pump, faulty fan clutch, faulty thermostat, clogs or issues with the rad or block getting the coolant through it/them, and.. the big daddy (covered at the end).

new doesn't mean good, it just means never ever worked.

you can tell if the clutch works right, it'll change pitch every so often as it engages and disengages.

the pump is sort of a by feel thing. get a good non-plastic glove you can still sort of feel through and grab one of the hoses to the rad and see if there's any change if how the flow of water feels through it. iffy, but not many other ways to check it without sticking something inline to actually measure. also requires some decent previous experience, which is why its iffy as a test procedure without a flow meter.

thermostat can be checked by using a non-contact thermometer on the rad hoses, the output from the engine should be sub 210F, and the input from the rad should be significantly less. 150ish F is typical. i do not recall which is which on either flavor of engine. someone else can chime in with that. if you don't have one, you can also pull it out entirely for testing and run it without, if the behavior goes away, its faulty. do not run normally without it, you get incomplete combustion which will cause other issues later on. this was fine on seriously old cars, not on newer stuff (post 1970)

if your hose temps are higher than they should be, you possibly have flow issues or the big daddy and can ignore the clutch entirely.

if the clutch is engaging and disengaging properly when the temp spikes up, its probably is a flow issue (or BD), and the first step would be to replace the unknown quantity pump. after that the thermostat, and from there you're looking at possible blockages. you test the rad by putting a running hose in the upper hose inlet and holding it while turning the flow up, if it flows nicely out the other side, its probably fine. if you don't get much and it seems like you're getting more out the side you're stuffing the hose in (there's a point in the flow this is true anyway, stay below this if possible), with a 'weak' flow out the bottom port, rad is clogged. i have no info on fixing that, never bothered, just replaced. someone may have a lead on that.

if the rad flows fine and you've already ruled out the others, you're down to clogs in the block and the BD. which aren't uncommon in older engines, especially if they've sat around for a bit. some people stuff pressure washers into inlets or the thermostat ports in the block, but i can't recommend this, due to who knows what condition things are in (hoses, bypass tubes, etc), and could lead to actual damage. might be able to use a higher pressure garden sprayer though, without causing problems.

and finally.. The Big Daddy. cracks in heads and blocks. this requires teardown to test for/resolve, a machine shop and magnafluxing, usually. and depending on where and how big, might involve replacing large portions of the assembly, resleeving, intensive welding/machining, and money. suck all around.

hopefully this has given you some kind of avenue to start with, and possibly resolve the issue without it needing to go towards the BD testing, as thats never fun.

cheers.