Are there timing chain specific chains? I believe Wipperman may have marketed a tandem sync chain, but there was nothing special about it other than the length. Larger-volume shops will tend to buy chain on a spool and just cut both drive and timing chains to length and you can often times buy chain by the foot from them for less than the cost of buying two standard length chains to splice into a timing chain.
Wouldn't a wider, beefer chain make sense for the timing chain. Again, sync chains are low-tech and aren't subjected to significant loads except on multi-seat tandems like triplets, quads and quints where the rear-most chains carry exponentially higher loads with each additional rider. However, once again, it's the drive chain that takes the real abuse, so any chain will work. That said, if someone didn't mind the added weight and slight up-tick in drag they could most certainly use a pair of 1/8" track rings with a 1/8" track chain, which would be bomb-proof and fairly long-lasting. Going the other way, a gentleman in Florida has been experimenting with a kevlar reinforced belt-drive system that is nearly maintenance-free, incredibly long-lasting, lighter, and nearly as efficient as chain drive.