I have the same type of remote start. I hit the lock button 3 times and it starts. The unit cost $99 on eBay from a company called Fortin, I believe. Quick and easy install. The only issue is that now the red circular security light flashes after starting but it didn't used to. This has only started happening after I had a reflash done for the clock issue, it seems.

When you hit the lock button 3 times does the jeep honk 3 times too?

Sound Horn with Lock
This feature will cause the horn to chirp when the doors are locked with the transmitter. This feature can be turned on or turned off. To change the current setting, proceed as follows:

• For vehicles equipped with the Electronic Vehicle Information Center (EVIC), refer to “Sound Horn with Remote Key Lock,” under “Personal Settings (Customer Programmable Features),” under “Electronic Vehicle Information Center (EVIC)” in Section 4 of this manual.

• For vehicles not equipped with the EVIC, perform the following steps:
1. Press the Lock button on a programmed (i.e. functional) transmitter for at least 4 seconds, but no longer than 10 seconds. Then, press the Panic button while still holding the Lock button.
2. Release both buttons at the same time.
3. Test the feature from outside the vehicle by pressing the Lock button on the transmitter.
4. Repeat these steps if you want to return this feature to its previous setting.