'01 and '04 license plate lights on rear bumper interchangeable?

Hi, I am new to this forum and I see there is a lot of knowledgable ppl here so hopefully someone knows the answer to my question and is nice enough to take the time to post it.  I have a 2004 Blazer 2dr. I just put a new rear bumper on it and it needs the whole assembly for the license plate lights (left and right sockets, the harness...) on the rear bumper.  I found used parts that are off a 2001 Blazer that can't be returned so I would like to know if they will fit my '04 before I buy it?  Thank you for all answers in advance.

UPDATE: Ok, so I got the parts and everything fits perfectly. 
 
I have a new problem though, the new licence lights don't work.  I put brand new bulbs in and I checked the fuses and everything looks good.  I also found that the hitch wires don't work.  The car had a rear collision, is there a chance that a module or something got damaged back there causing both of those things not to function?   Thanks. 

how bad of a rear end accident???   any pics of the b4 crash???

No pics of b4 crash only after :(