How too reprogram my avital remote with the rpn 7111l

Since this is not a factory remote start, you will need to find an installer that is local to you, or maybe you can reach out to Avital for assistance. https://www.avital.com/

Remote Starters have to bypass the anti-theft software. disconnecting the battery, broke the programming. You will need to take it back to the installer.

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I have 1987 toyota 4runner model and I keep servicing and when needed repair it on my own. worth it !!!

same here my Auto starter Avital 7111L happened this morning never happen before , just replaced the battery and it happens press the remote start it start right up but shut down after 5-6 second and restart by it own like 3 times , i like the way the gentleman on top comment said you need to drive around at least 15 minutes for it to relearn the system again , my brother Honda CRV 2017 did the same thing after replaced the battery a lot of light show up on the dash but after driving around for 15-20 minutes it go back to normal again hope this help .

try using a scan tool to reset the system

It sounds like the positive light feed is back feeding the flasher relay.
With your remote starter, can you select negative instead and wire to the negative wire instead? If not, you can use a standard automotive relay as an inverter:

http://images.the12volt.com/12voltimages/pos2neg.gif

will it start with the key?

Sounds like you need to call Avital to help you reprogram your remote, they offer 24/7 phone support. call them they will walk you thru it on link below

http://www.avital.com/Support/