Local Carrier Stamp - L-02 Or L-05

Had never seen Local Carrier Stamps before, and came across this one in my acquired collection as I was putting stamps into albums.

Looking for ID assistance or links to resources about this stamp (or series).

This stamp was with another that was identified as L-03 (which is the reprint from 1875, not the original from 1851), so my suspicion is that this stamp might be L-05 (the reprint from 1875).

Appreciate any insights, opinions.

Below is the footnote in the Scott Specialized. Given the condition of your paper it may be impossible to call this an LO2. Is that gum on the reverse or are you just showing how brown the paper is?

The first two reprintings of 10,000 each of the Eagle stamp are on the same hard white paper used for
special printings of the postage issue. Stamps from the second reprinting were printed with ink that fluoresces
green. Stamps from the third reprinting are on thick wove paper using ink that does not fluoresce.
Reprints may be differentiated from the originals under ultraviolet light by the whiteness of the paper. Nos.
L03-L06 are ungummed, Nos. L01-L02 have brown gum. No. LOI was printed on a somewhat yellowish
paper.