I think you'll find that the rounded appearance is most likely a product of being stamped into the metal, or from wear and tear on that same metal.
OTOH, the centre bar of the E looks much shorter in your sample than in Gotham. If you can live with the E being slightly different, I've found what appears to be a free version of Gotham Light that actually is rounded here.
Cheers!
PS -- I've asked the mods to merge this thread into the existing, long-running Font ID thread.
Thanks, that looks more like it, I really am grateful to all your help.