Which action does the FortiGate take when link health monitor times out?

The link health monitor is tied to a specific next-hop gateway; it's the routes using that gateway that are affected, not necessarily all routes to a destination subnet.

Increasing the administrative distance of routes would make them less preferred, but the direct action for a failed gateway is typically to remove the routes rather than just modify their distance.

Increasing priority values would make routes *more* preferred, which is the opposite of the desired behavior when a link or next-hop fails.

A link health monitor is configured to periodically check the reachability of a specific next-hop gateway. If the monitor times out (meaning the gateway is unreachable), the FortiGate's primary action is to remove all static routes from its routing table that are configured to use that failed next-hop gateway, effectively blackholing traffic or forcing it to fail over to another path.