glow plug light

Hi Guys, I have a 91 350sdl and the glow plug light doesn't come on untill the car runs for about two minutes, then stays on for about 45 seconds then goes out. When I start the car I wait about 30 seconds and she fires right up , so plugs must be working. However the remote starter will not start it, It tries to start before the glow plugs have a chance to warm up. Does run rough for about 30 seconds. Appreciate any suggestions where to start checking. Thanks