Question: What specifications do I need to look for in a class D vehicle amplifier so that I can run it for 8 hours using an 18V 5Ah rechargeable tool battery.

I need to operate the amplifier at full power for 8 hours. 

What power rating could I hope to support?

Answer: 
Ah / A = Time in hours, so choose a power amp, find out its current draw in amps and plug in the numbers...

You can also do Ah / hours = amps which gives 5 (Ah) / 8 (hours) = 0.625 amps to run your power amplifier, a small one then.

Note I ignored the voltage difference and also that you probably won't get the full stated capacity of the battery in Ah..
18v \* 5ah = 90 Wh (this is the energy you got)

90 Wh / 8h = 11.25W (this is the max power you can draw for 8 hours)

You need an efficient amplifier, so it will be class D. 

Suppose 90% efficiency. I'd go with a 10W class D amp, allowing a bit of headroom.