I’m guessing the sign dates from the 1950s or 1960s? Then there is little likelihood that it corresponds to a typeface used for printing. This article explains why.
Another post on this forum provides additional context and reference links (though many rely on archive.org, which is currently offline). In short, a number of companies sold metal and wood letters expressly for use in architectural signage, and though many of the styles on offer resemble commercial typefaces, they weren't exact copies of them.
The Spanjer Brothers Company of Chicago offered a very similar style (“Kabel Style”) in its 1961 catalog:
You will likely have to use what I posted as a guide to create the new lettering as vector artwork, so you can replicate the look of the existing signage.
Message me directly by clicking on my username and posting on my wall (include your email address), and I can send you the higher-res PDF of the Spanjer catalog that I downloaded from archive.org earlier this year. I'll then delete your wall posting so your email address won't be on permanent display (as it would be if you posted it here).
