Honoring the elderly in an elevator?

Shalom u’vracha 

The mitzvah of “and you shall honor the presence of the elder” includes only standing up in his honor. 

This mitzvah applies in any place where a person is seated and the sage or elder comes in, except in a degrading place, such as a bathhouse. 

Apparently, your question relates to the law explained in the Gemara (Berachot 47a), “They show honor at the entrances,” meaning that one allows a Torah scholar to enter first. And there the Gemara states that this applies only to an entrance that has a mezuzah, or “an entrance that is fit for a mezuzah,” even if it does not actually have one — such as synagogues. 

From this it is clear that whenever we are dealing with a dignified place, there is a mitzvah to let the sage go first, to the exclusion of a degrading place. 

Accordingly, an elevator, which according to many poskim is exempt from a mezuzah, but is not a degrading place, involves a mitzvah to allow the sage to enter first. 

Shulchan Aruch, Yoreh De’ah, siman 244, se’if 1
It is a positive commandment to stand before every sage, even if he is not elderly but a young and wise man, and even if he is not one’s teacher (as long as he is greater than him and fitting to learn from). And there is likewise a commandment to stand before a gray‑haired elder, that is, one who is seventy years old (even if he is an am ha’aretz, provided that he is not wicked). 

Babylonian Talmud, tractate Berachot 47a
“One shows honor only at an entrance that has a mezuzah.” Where there is a mezuzah — yes; where there is no mezuzah — no. If so, in a synagogue and a study hall, where there is no mezuzah, should they likewise not show honor? Rather, say: at an entrance that is fit for a mezuzah. 

Mishna Berura, siman 90, se’if katan 62
They show honor at the entrance of the synagogue so that the great person enters first, since it is fit for a mezuzah.