You can build your own flipper for about the price of a 240v timer, and use this design for other applications. e.g. converting a 120v timer to a 240v timer.
Parts:
120v timer
Potter & BrumfieldKUP-14A15-120 relay & socket (doesn't have to be this make but P&B is common and reliable)
cord with 2/3 prong plug (depends on the timer you are using and want to ground)
electrical box or board to mount (din rail looks pro if using more than one relay)
Assembly:
mount the relay base
wire the cord to the A terminal (neutral), B terminal (110ac) You have just wired the coil of the relay.
Application:
Flip Flop: Output of the ballast will go to the common terminals 9,8,7 (yes you will have a spare)
NC (timer off) terminals 3,2,1
NO (timer on) terminals 6,5,4