That's definitely not a font. It was drawn by hand, by someone not exceptionally experienced in designing letters.
I would guess that the lowercase was based on something like
Century Book Condensed, and the capitals were an invention of the designer. It's very unusual to see ball terminals on an uppercase C and S, and the curved stem of the T is something you would virtually never see in a regular serif font.
I would suggest either you find a way to precisely trace the old
signs, if the client wants to retain the amateur/rustic/hand-drawn look, or find a type designer to redraw it with some improvements and updates to make it look a bit more well-drawn.