Town mayor Ken Sanders told last week's council meeting that he would like it to become 'a permanent memorial' to the Jubilee, but was at a loss as to where it should be sited.
Options ranging from in front of the Town Hall to the new underpass proposed for Plymouth Road — which could be renamed Jubilee Underpass — were all discussed by councillors.
The general feeling was that the beacon — currently in storage awaiting a decision on its fate — should remain at The Pimple.
There were fears of vandalism, but Cllr Peter Donkin suggested it could be bolted down in a similar fashion to some new seats which had been placed there.
Cllr Roger Mathew said using the beacon for a specific purpose and then moving it 'didn't quite stack up'.
He said if it was kept where it was lit, it could have a plaque explaining why it had been erected — so it should stay at The Pimple.
Councillors also thought that if it stayed there it could be re-used at some future occasion.
A decision will be made at a later date after councillors have given 'serious thought' to the matter.