Does the other party know you’ve tracked their phone

If your contact has shared their location with you - see Find friends and share your location with Find My - then their location will always be shared until they decide to cease sharing. This can be a temporary pause in sharing after which they resume location sharing, or a withdrawal of permission to share in which case they will no longer appear in your Find My.

Find My will continuously update a shared location. Just because you have looked at a location for a moment does not change the status of their sharing nor does it require a report that you have checked the location.