1966 Valiant Signet Park/Signal lamp problem

First things first: there are many different sockets for any given kind of bulb, and they are not all the same. Not only are there different installation/attachment styles, but also a bunch of different focal lengths. This is really critical; the bulb has to be placed exactly where the lamp was designed for it to be. "Close" isn't good enough. "Fits the hole" doesn't cut it. Move the bulb by as little as 1/16" and the filament is no longer where the reflector/lens optics are engineered to see it, so output from the lamp nosedives (reflector no longer lights up, you just get meager light directly from the filament through the lens).

Many of the sockets are no longer available, if they ever were, in the aftermarket. Some lamps, such as the ones you're working on, do not have sockets designed to be replaced. You can refurbish the original sockets. You'll need two of these (the single-filament equivalent for things like back-up lights is this). Use a small wire brush on a Dremel tool to clean the socket housing/cylinder.

Before you install the new parts, clean the reflectors with alcohol, stuff a wad of masking tape in the socket hole and shoot 'em with a good brand of "chrome" spray paint.

Use new 1157A or 1157NA bulbs with a nickel-plated (silvery-colored) base, not plain brass -- plain brass corrodes, sticks the bulbs in the sockets, and makes a mess. For extra corrosion protection, apply some silicone grease to the bulb base and contacts. Not a whole lot, just a light film.