Just purchased my first Lexus a couple of weeks ago -- 1997 LS 400 (had a little over 81,000 miles on it). Purchased it on e-Bay and actually had never even driven a Lexus. Great car! And this is a great resource for a Lexus novice such as myself -- thanks!
Re. the flashing cruise light -- the dealer where I bought the vehicle advertised a full tank of fuel with the purchase. The tank was only a quarter full when I picked it up, so he gave me cash to fill it up before I headed home with the car. Filled up, got up to speed on I-10 heading east from El Paso where the speed limit is 80 mph. Pushed the cruise button, light comes on and it holds speed for about 4 or 5 seconds then drops control of speed and cruise light begins to flash on on and off. Tried stopping the car, turning it off, and then setting the cruise again when I was back on the road. Same things happens. I'm thinking -- bought it "as is" and "as is" means the cruise isn't working right. Drove home w/o cruise.
Told a friend who used to be the service manager for a local car dealership about the problem and he said that he had seen his pick-up's cruise do the same thing when he pulled his camper trailer into a stiff wind -- his truck didn't have enough power to keep the cruise going. I went back to the Lexus manual and noticed that the LS 400 requires premium fuel -- and realized that I had put regular fuel in when I filled up in El Paso (as I said earlier, I had never driven a Lexus before). This made me wonder if the car was doing something similar to my friend's truck when it was underpowered.
My tank was half full of regular fuel, so I filled up with premium. Took the Lexus out for a spin on the open highway and tried the cruise. It worked perfectly and has ever since (with me using premium fuel now). My conclusion in the case of my vehicle is that it was underpowered running on regular fuel and that is the reason for the cruise problem.