How do I know if my Leak detection pump is working?

So I have been working and working on my P0455 diagnostic trouble code. I have looked at all the vacuum lines, done a smoke test and am unable to find any leaks. I have been told that my Leak Detection Pump is most likely the cause of my problems. My local Jeep stealership wants over 400 bucks for this thing, and it may not even be the problem. I got a leak detection pump from my local Pull-a-part for less then 5 bucks, shut off the check engine light, and only 3 days later it is back on with the same code. I am told that these pumps go bad quite frequently. How can I tell if mine is working properly? The one that was on my XJ was making a squeeking noise when I first started the vehical in the morning, but it when away after the jeep got warm. The other one is dead silent, does this mean that it is dead? Both of them, I can not blow or suck air from where the vacuum line hooks up, but where the large tubes go, air passes freely. When I smoke test at the port next to the purge valve, I get smoke from the small air filter connected to the LDP. Is this normal? I can block off the end of that hose and smoke test and get no leaks anywhere else. My stealership won't offer any information unless they are the ones fixing it. Thanks for any help! -Jason

I went through the same thing on my Mom's 01XJ. For me, it was more of a process of elimination like you have been through. And you are sure your purge valve is good? 400 bucks is INSANE! I think I paid about 70-80 for hers...can't remember if it was rockauto or locally?

The pumps on my 2001 Jeeps and my 2001 fancy foreign car can all be heard from the cockpit though it's faint. Putting your hand on the pump should feel a tick-tick-tick sound when it's pumping.
It only pumps when gas level is below maybe 7/8 or less in the tank and above some modest temperature (50?) and only after startup.

Both my 2001 Jeeps had cracks in the single-wall rubber hose connectors that join the gray PVC piping going to the charcoal reservoir. There are 2 connectors on the 2001 models, one near the firewall and another further aft.

My early indication of hose cracks were the 'small leak' code which could go away for awhile after clearing. Wasn't consistent at first.

Good luck!