If you eliminate the requirement that the lamp uses a Fresnel lens, then you also eliminate the requirement that the pole have a bend. With those two requirements gone, your search for a suitable pole lamp is simplified
ASIDE
The use of a Fresnel lens on the white all-round lamp will focus or intensify the strength of the emitted light toward the horizon. If the lamp is not oriented properly, the emitted light won’t be sent toward the horizon. That is why the pole is bent on the lamp in Figure 1, and the bend is matched to the slope of the boat's transom, which on small Boston Whaler boats will be about 14-degrees.
A much simpler lamp design just uses a diffusion lens, and projects the light without creating a narrow and focused beam.
Also, the the lamp seen in Figure 1 appears to use the mounting method of having two circular mounting fixtures installed on the transom. This method is common on classic Boston Whaler small hulls.

- Fig. 2. Pole lamp mounting detail as seen on older small Boston Whaler open hulls.
- poleLampMountingDetail.JPG (60.27 KiB) Viewed 356 times
The ID of the circular mount is 7/8-inch, typically.
The only source for that exact OEM lamp will be from an older classic small hull. It would be unusual for an owner of an older 13-foot to want to sell just OEM the pole lamp from his boat.
There is a similar lamp being made by PERKO. See
https://www.perko.com/catalog/navigatio ... -in_mount/Instructions for the above lamp:
https://www.perko.com/images/catalog/pd ... t.%20(USCG).pdf
The above lamp has a 7/8-inch diameter pole. It is available in three pole lengths, the longest at 34-inches
An important consideration is the length of the pole itself. To comply with the USCG regulations, the white all-round lamp should be located so the light is showing from 1-meter above the light from the sidelight lamps. On a classic 13-footer, the sidelight lamps are almost always combined into a single red-green combined lamp, and mounted at the bow on centerline. The white all-round lamp then needs to be carried 1-meter higher than the sidelight lamp at the bow.
Unless your goal in restoration is to have the museum-accurate completely original c.1960 13-footer, there really is no need to insist on having the OEM navigation lamp for the white all-round lamp. Just about any pole lamp could be used, and if using with the OEM circular mounting, then the only requirement will be the OD of the tubing, if it needs to fit into the existing mount.
If the goal is just to allow a boat to be properly operated while underway or at anchor in darkness , then you can install a different style white all-round lamp.
MORE ABOUT OEM MOUNTING
The typical OEM mounting method on a smaller Boston Whaler uses two circular clamps. See Figure 2, above. Boston Whaler used that mounting because of the unique Unibond hull design. Normally a navigation pole lamp would be mounted to a socket fixture on the stern deck, and the wiring would be accessible under the deck. But on a Unibond small open hull, there is no access under the hull gunwales, so the lamp mount as shown in Figure 2 was always used.