Let’s clear up a few misconceptions.
For anchoring, the COLREGS require an all-around white light meeting the following (I've scraped out some of the stuff that only applies to large vessels, to save space):
COLREGs
Rule 21 - Definitions
(e) "All-round light" means a light showing an unbroken light over an arc of the horizon of 360 degrees.
Rule 22 - Visibility of Lights
The lights prescribed in these Rules shall have an intensity as specified in [Section 8] of Annex I to these [Regulations | Rules] so as to be visible at the following minimum ranges:
(c) In vessels of less than 12 meters in length:
(i) a masthead light, 2 miles;
(ii) a sidelight, 1 miles;
(iii) a towing light, 2 miles;
(iv) a white red, green or yellow all-round light, 2 miles.
Rule 30 - Anchored Vessels and Vessels Aground
(a) A vessel at anchor shall exhibit where it can best be seen:
(i) in the fore part, an all-round white light or one ball;
(ii) at or near the stern and at a lower level than the light prescribed in subparagraph (i), an all-round white light.
(b) A vessel of less than 50 meters in length may exhibit an all-round white light where it can best be seen instead of the lights prescribed in paragraph (a) of this Rule.
(c) A vessel at anchor may , and a vessel of 100 meters and more in length shall, also use the available working or equivalent lights to illuminate her decks.
Code of Federal Regulations (CFR)
Section 8, Annex 1
84.17 Horizontal sectors.
(b) All-round lights shall be so located as not to be obscured by masts, topmasts or structures within angular sectors of more than 6 degrees, except anchor lights prescribed in Rule 30, which need not be placed at an impracticable height above the hull, and the all-round white light described in Rule 23(d), which may not be obscured at all.
(c) If it is impracticable to comply with paragraph (b) of this section by exhibiting only one all-round light, two all-round lights shall be used suitably positioned or screened to appear, as far as practicable, as one light at a minimum distance of one nautical mile.
My interpretation has always been that Rule 30 requires, for an anchored vessel less than 50 meters in length, an all-around white light, or two that cover the same 360 degree arc, mounted where it can best be seen, and deck and working lights
are allowed (and are definitely required on large vessels). This all-around white light must be of an intensity so as to be visible for 2 nm or greater (vessels under 12 m), which does not say that it actually has to be seen from 2 nm away – just that the intensity has to allow it (within a +/- 5 degree offset from a horizontal plane, which is in the Annex, but I didn’t copy it) in presumably clear weather with no obstructions to visibility, like the curvature of the earth.
The all-around white light has to be all-around, but is permitted to be mounted or supported such that there is no more than a 6 degree arc that is blocked. A 3” wide mast that’s 10 feet away only blocks about 1.5 degrees of arc, and unless it's glass-flat water with zero wind, a hanging light will move around a bit, effectively narrowing the arc even more, if intermittently.
There is no requirement for mounting height (for small boats, using a single light or close-paired set of lights acting as one), nor is there a requirement for permanent mounting. In fact, many cruisers use oil lamps (which have similar intensity requirements). It is VERY common for cruisers to hang the anchor light, oil or electric, from a spar or stay, in order to bring it down to where it can better be seen in close quarters, and/or serviced (in the case of oil lamps).
My last boat had a 56 ft bridge clearance, not counting the antenna and wind instruments, and the mast-top mounted, 2-bulb anchor light (combo masthead and anchor) would not be seen by other boats in close proximity, especially if the skipper is under canvas or roof, and anyone even close to it would be far below the -5 degrees from the horizontal, resulting in a much dimmer appearance. In a protected anchorage, far from shipping lanes, 56 ft in the air is not what I’d call ‘where it can best be seen’. 10 ft off the water is right in the eyeballs of small boat drivers. Since I've only (ever) anchored in small, protected waters, I don't see the need for having the anchor light 5-1/2 stories in the air. On my modest

boat, 33 ft or so is still pretty up there - fine for seeing from far away, but useless when the fireworks are over and the powerboats weigh anchor and make the mad dash en masse to the river mouth.
As far as my wooden kludge arrangement, that’s only so I can use the anchor light as a masthead (steaming) light, when the mast is laying down in the crutch and pinned to the bow rail, for operation on the Erie Canal. The factory masthead light is riveted to the mast and aimed at the airplanes, and the cord wouldn’t reach anyway, so this is what I use. There’s a 12V socket at the helm that I plug into. It meets the letter of the COLREGs and CFRs, takes all of 30 seconds to mount, and it’s not permanently mounted to the mast where it would get in the way when sailing. For anyone NOT operating at night with the mast down, it's not relevant, and it has nothing to do with using the anchor light as an anchor light, which also takes all of 30 seconds to implement using a halyard and loop around the backstay.
The OP asked about alternatives to a permanent mast-top anchor light, so what I offered fits the bill as I interpret the COLREGs and CFRs.