I know of four methods of starting a 3 strand eye splice:
1) The old faithful - bend eye to the right
These all can be so oriented (just flip the one bend-to-left one over),
for an equal comparison.
As for others, hmmm, there is at least the method in which one splits the
trio of strands for the length of intended tucking AND eye, and re-lays one
against the two in opposite directions ("Flemish"?), which should bring
to-be-tucked ends back with different (from above) placement. (With a
PP soft-laid cord in hand (i.e., one that is easily re-laid, with its stiff,
shape-retaining ("memory") fibres), I'm now contemplating how to do
the tucks (and not seeing a compelling course)-: .)
I recall at one time thinking to try to figure out--but not following through--
if there were tuckings not shown in
ABOK where one reversed the
parts of the rope--i.e., see the
end being tucked as instead the SPart,
and then how was it that the former SPart's strands came into IT (this
requires that the given tucking doesn't alter the relation of the strands
from the raw-rope order, changing positions).
Then, beyond the tucking start, there's the continuation--over & under
or around (sailmaker's), and with some opening/unlaying of the strand
to *flatten* it or not. And the finish, where one might try, e.g., a by-strand
taper (what Brion called "California taper", I think--aka "West Coast t.")
At one point I took some 5/16" laid rope (short bit) and brought the ends
together to marry in a sailmaker's splice sort of way, thus creating three
fattened strands, which I think short-spliced into a 3/8" SPart. That
was fun, and consumed some spare bits of no great importance.