Does the security indicator light continually blink when armed?

Yes, the security light will continually blink ( about once every 10 seconds or so ) while the security system is armed. I wouldn't be too concerned about draining the battery though, the light is so tiny ( and may even be an LED -- don't know for sure ) that the light would burn out before it drained your battery significantly enough to notice. If you are experiencing a problem with your battery losing charge and are thinking that the security system may be to blame, I would recommend that you have your battery and charging system checked instead ( AutoZone and Advance Auto Parts will usually provide this service free of charge ).

how do i reset the security on my frontier to get it to start and run

yes, thats why you need a good battery perhaps buy a new one

My 2019 Nissan Frontier has started the Security light blinking every second yesterday instead or every 10 seconds. Why is this happening. My one year warranty ran out the day before?

fuck all lights and buzzers, how about a return to cars that don't try to save me, techno =BS