I actually figured it out. No need for the lever, no 'studder' either. Using the same 'hardware' as the usual rapid pulser(1 reciever, 1 emiter, 1 manager) The way it works is on the emitter, I use one side to create the 'rapid pulser' circuit, and another as a variable side. The variable side is set to pulse for one second, and gets its pulse duration updated with each 'cycle' of the rapid pulser. I then use a interval trigger to check to see if the 'variable side' is off, and if so restart the pulser:
t:Int Check Rs - Trigger(Interval)
Default
c:Side Off - Redstone Condition
Sides: 'variable side' (pick one, other than the side facing the redstone reciever)
t:RS Receiver - Trigger (Redstone) - Redstone Receiver
e:Rapid Pulse - Redstone Emitter
Sides: Side facing the Redstone Reciever
Output: Toggle
e:Var Side - Redstone Emitter
Sides: 'variable side' (the same used for the Redstone Condition)
Pulse: Do emit Pulse, 1 second, Extend Old