I think you need to determine a new process for what defines a ticket needing a response, since as you know your current method is flawed because of how LastUpdated and LastUpdatedBy works.
So, in your environment, what else can you use to determine that a ticket needs a response? A status perhaps? If this is for a newly created ticket, generally I’ve seen the status stay “new” until it’s responded to, in which it transitions to “open”. In that case, searching for “new” would solve your problem.
In my environment, I set my custom status to “waiting on customer”. When the customer, or more specifically the requestor responds, I have a scrip that changes the status to “followup”. Then I know it’s waiting me to respond. Not sure if that fits your environment, but just something to consider.