I've tried to use the latest geth with
--light mode. It gets new blocks not very fast, but I could send transactions successfully. So I think it's useful!
What command should run parity in this mode?
Parity does not support light client mode, yet.
Older versions did have a
light pruning mode, but that is something different, and not to be confused with.
The answer to your actual question is provided in the previous post by 5chdn... (i.e. You can't.)
However, if you just want a way to sync (more) quickly, then in Parity you could try
parity --warp, as explained in this previous thread.