I used to install at Circuit City back in the day. Yes, you can put a remote start on a manual transmission. I put one on my 5-speed 95 Grand Am. However, to do it safely, you need to buy a remote start/alarm that is designed for a manual transmission. The alarm units that are made specifically for manual transmissions have additional interlocks that must be met in order for the car to start.
The Alarm/remote start I had was a:
(Clifford Ace 7500)
The way it worked on my Grand Am was that I had to:
1. Car is currently running
2. Set Parking Brake
3. Put the car in neutral
4. Activate remote start
5. Remove the ignition key (car stays running because remote start was activated)
6. Open car door and exit the car
7. Close car door. (you are now outside the vehicle but the car is in neutral and still running)
8. Set (arm) the alarm. (The car doors will lock and alarm will set and the vehicle will turn off).
This sequence had to be done everytime you exited the car for the remote start to be enabled.
The whole purpose of this sequence is that you know for sure that the car is left in neutral.
Now anytime you hit the remote start button on your keypad, the car will safely start in neutral.
Exceptions: If the car alarm is disarmed (unlocked), the remote start is disabled.
If the alarm is triggered for any reason, it will disable the remote start.
The only problem putting this on a Jeep is that Jeeps are convertable tops.
Someone could reach inside and put the car in gear without the alarm going off.
You could add a proximity sensor to the alarm but from my experience, they cause to many false alarms when people walk too close.
If your Jeep is equipped with a transponder in the key. Then any ignition type key that came stock with the vehicle will work to bypass the facory anti theft. You can get an extra from the dealer, but they are pricy. I doubt that a $6 dollar vallet key has the chip inside it. If the key has the big grey grip at the base, then it probably has the chip.
Also, maybe they have come out with a new module that doesnt need the key to stay in the dash. I know that for installing on Ford vehicles, you only needed the key to program the bypass module during the installation. Call your local install shop and find out.
There are probably alot more remote start/alarm models available these days. Just make sure they are (manual transmission compatable.)
This is also something you want to have installed professionally.