Where does the term בית עולמים come from in reference to the Temple?
2 Answers
I don't know if it is the main source - but an early source can be found in the Mechilta
עד שלא נבחר בית עולמים, הייתה ירושלים ראויה לשכינה, משנבנה בית עולמים יצאת ירושלים שנאמר (כי בחר ה בציון) ואומר 'זאת מנחתי עדי עד' [תהילים קלב]
Before the Temple was chosen, all of Jerusalem was fit for (the reposing of)) the Shechinah. Once the Temple was chosen, (the rest of) Jerusalem was excluded. As it is written (Psalms 132:13-14) "For the L rd has chosen Zion … This is My resting place forever."