flag-sign of a tavern
帘 centers on a hanging cloth sign used to mark a tavern or shop. The meaning is narrow and concrete: a flag-like banner that signals a drinking establishment.
帘 combines 穴 (hole, opening) and 巾 (cloth), suggesting a cloth hung at an opening, consistent with a tavern sign. The exact historical development is uncertain.
Imagine a cave-like opening (穴) with a cloth banner (巾) hanging down: that cloth is the flag-sign of a tavern, marking the entrance.
For レン, picture a tavern sign made of a long linen cloth: linen -> レン, and the cloth hangs as the flag-sign.