I noticed some similarities between the aish tamid (Leviticus 6:6) and the ner tamid (Exodus 27:20) and wondered if there's a connection between these two and if they share similar symbolisms?
The verse in Exodus 27:20 is translated as follows:
וְאַתָּ֞ה תְּצַוֶּ֣ה ׀ אֶת־בְּנֵ֣י יִשְׂרָאֵ֗ל וְיִקְח֨וּ אֵלֶ֜יךָ שֶׁ֣מֶן זַ֥יִת זָ֛ךְ כָּתִ֖ית לַמָּא֑וֹר לְהַעֲלֹ֥ת נֵ֖ר תָּמִֽיד׃
You shall further instruct the Israelites to bring you clear oil of beaten olives for lighting, for kindling lamps regularly.
The word תָּמִֽיד is translated as “ regularly” by Sefaria and that is the way the commentators understand it.
(E.g. Rashi says
להעלות נר תמיד כל לילה ולילה קרוי תמיד
it is lit each night which is called תמיד.)
תָּמִֽיד describes when the light is to be lit and does not describe a specific light that has to be lit always.
The verse about the aish tamid (Leviticus 6:6) is an instruction to the people of Israel to make sure that the fire on the altar never goes out. There is no object in the verse called the Aish Tamid.
The word תמיד in Exodus 27:20 links to the word תמיד in Leviticus 6:6 to indicate that the regular lighting of the light must be from the fire on the altar as Rashi points out.