I have seen this in my 1965 Plymoth. It turned out to be that I put a 2057 bulb in and the original bulb was an 1157. In 1984 most cars went from a 12 Volt system to a step down and a 5 Volt system. But the car manufactures still had lots of the old housings for the bulbs. So they made a lower voltage bulb for the same housing. The new bulbs fit in right but lower resistance. The result is the system tigers the blink off and blink on much faster. My guess is one or all of the bulbs are a more modern bulb then the car was designed for. The first thing I would do is verify with the owners manual if you have it what the proper bulb is for the car. Then order the correct bulbs.

Sorry I just reread that you used the correct bulbs. The Issue is there is too much voltage going to the system. If you add a resister somewhere in the system it will slow. My guess is that you replaced something that was designed for a 5 volt system (newer car)