For mice, it would definitely be droppings and sightings of them. With termites, most people don't know they have them until they see a termite swarm. For carpenter ants, finding the frass (the remains of the wood they leave behind as they excavate) or just seeing ant activity.
Mice droppings are definitely an indication of these pests. Obviously, sightings of ants as well as seeing and hearing stinging insects around should be huge red flags.
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