Could this be reverse switch?
 

Ok well few days ago Im about to leave the house in the morning and crank the car, it cranks normally like it does every morning but with a very slow feeling. 2nd try nothing. Than all I hear is the fast clickin of the starter.
I assume it's the battery so I jumped it and worked fine.
I than made my way to the back of my car and notice the reverse lights are on when car was in neutral.
I than decided to take the bulbs out ( they were hot as **** ) I went to put them back in later in day and they turned on right away.
Could this be the reverse switch in trany is faulty?
04 74k miles manual
If you need more info let me know

Could be or a chafed wire.

They were on my neutral switch.

Yeah, it could be a reverse switch... But I'm leaning towards a wiring issue, since the Reverse Light switch should have no power going to it with the key off.

I presume this is your concern, that something is draining the battery. Yes?

I"ll see if I can find an rx-8 electrical distribution schematic. Your best bet is probably a stuck relay contact that is supposed to be normally open but stuck closed.

Jack up your car, put jack stands under. Climb up under on your trans yowrards front top you'll see a white connecter and black connector. White is neutral, black is reverse. Put your car in neutral. Disconnect your black connector measure your ohms with a fluke in the connector. It should read open. Put it in first should read open. Repeat above steps until reverse. In reverse it should read closed (you'll sEe numbers) if it shows closed while your in neutral or any gear other than reverse then your switch is bad. If it reads out good then definately wiring.

Ok thanks guys I'm gonna check the reverse switch today.
And yes I just don't want it to keep I draining battery that's why I took out the bulbs. I haven't touched anything where those wires go. What stuck relay? Where are they that come from the taillights?

There are no relays in that circuit:
Attachment 180899
Keep in mind that a lot of people here just throw out random thoughts without actually looking through manuals or schematics to give you the best advise.

Since the reverse lights should not receive power with the ignition off (refer to diagram above) you need to find where its coming from.
I would start at the reverse switch and see if you have voltage on the black wire w/ yellow stripe (ground to body).
This will tell you if the problem is upstream or downstream from that switch (placing bet on downstream).

Hence the quote probably a stuck relay or contact." I need to look at the schematic first." Not just a random thought. And of course a reverse switch is a contact indeed. I'm sorry I only have 12 years experiance as a nuke electrician on a submarine troubleshooting everything from reactor circuitry to the washing machine. And another 6 years behind that supervising 25 electricians at a civilian power plant troubleshooting a lot more detailed than any electrical schematic in the 8. I'm just saying. Anywhoo interested to here what you have found so farr