This might not answer your question perfectly and I also don't use Logic, but I know that some people like to use a separate click sound for sidechaining.

The reason is that the sidechain isn't so clean when your source signal isn't a nice smooth click. It's a little messier and unpredictable especially when you're trying to sidechain it super tight.

Sometimes I use a super short sine wave that isn't actually sent to the master (therefore is not heard) with no attack or release so it's a straight click that dips the lead or whatever nice and cleanly.