Trader has multiple spots it -can- spawn in on a map. Once you find it, that locks in that spawn spot for the trader only. Any other potential spots on the map will not have the trader.

That said

Sometimes they're extremely close. Sometimes they are very far away.

If you want to know exactly the places on your specific map it then I suggest using:

https://valheim-map.world/

Input your world's seed and tick the box for trader and see where it is on your map.

Otherwise, yes, you would need to explore the entirety of the map until the bag icon shows up on it.