Start or stop service automatic?

Assuming that you are referring to a service on a node, you should be able to do this with a sideband connection. If you cannot control the service directly from the sideband connection you can probably create a helper app (akin to an API) on the node (server) that can respond to the sideband request.

I will create pool for only monitor but not use for virtual server. Can I use sideband connection for this?

You can use an IP-address (node, VIP, public web site) or the name of a VIP for the destination of sideband connections. However, you cannot use a pool as the destination.

However, I assume that you will want to disable/enable the service on more than one server. If that is the case you wouldn't want to use a pool since that would connect you to only one server.

What you can do in an iRule is get the list of pool members and then you can iterate through those to target each node to toggle the service on each of them.

Can a sideband connection use for run script or command to start or stop on remote server?

You can restart a remote service with a sideband connection by triggering an action (e.g. script) on the remote server. Theoretically you could trigger restart the service remotely, but there can be serious security drawbacks.