Hi Bayrunner...let me first start off by saying I have NEVER been inside a Toy. 4cyl.

OK, now my e-advice <img src="/forums/images/graemlins/notooth.gif" alt="" /> It sounds like you've got 'valve tap' by the description you gave. This usually is pronounced when the engine is cold/er and almost all of the oil is in the pan, not the head.

After starting the engine up, you hear a tapping that gets quieter and quieter before going away, no?

[off-topic]This is actually very common on older engines as well as certain engines- for example my brother's 2000 Nissan Xterra has done this since he bought it. It gets progressively worse until I finally change his oil when it's 5k miles overdue <img src="/forums/images/graemlins/rolleyes.gif" alt="" />
Isuzu 3.2/3.5 engines fall under the same category as well and the most likely causes for all of the aforementioned engines is sluddge build-up in the oil passages. This can be remedied (or help at the very least) by runing a 0W oil through the engine for about 30 minutes and draining/refilling with "regular" oil.[/offtopic]

BUT

As to why this would be occuring on a newly rebuilt engine, I can't say exactly. There's a few thoughts that come to mind, but I really don't feel comfortable throwing out ideas that could be way off base.
The only advice I feel comfortable giving is to check your valve clearances or have the shop do it for you if it was rebuilt very recently. And if/when you go back to the shop, don't accept 'that's normal' for an answer <img src="/forums/images/graemlins/shiner.gif" alt="" /> because you know you've never experienced this before.

Since I'm practically illiterate when it comes to 22R's, RE's, etc etc. hopefully someone that is more familiar with this engine will chime in.

Good Luck! <img src="/forums/images/graemlins/cheers.gif" alt="" />
~R