[Bluegrass Conservative]

Why would they think the need for tents if they were just "seeing" into heaven?

A tabernacle is a place or worship. I took that as if Peter wished to build three places of worship (most likely altars) to Jesus, Moses and Elias.

[mother]

Actually a Tabernacle is a place of repose. A shelter.

[mother]

In a Catholic Church, the Tabernacle is the place of repose for the Blessed Euchrist. The actual presence of Christ.