imply emblem -> symbol
alias insignia -> emblem
imply military_rank_insignia -> emblem
imply blazblue insignia -> emblem

imply anchor_symbol -> symbol
imply sun_(symbol) -> symbol
imply flower_(symbol) -> symbol
imply diamond_(symbol) -> symbol
imply radiation_symbol -> symbol
imply mars_symbol -> symbol
imply power_symbol -> symbol
imply peace_symbol -> symbol
imply tomoe_(symbol) -> symbol
imply shapes -> symbol
imply konohagakure_symbol -> symbol
imply japari_symbol -> symbol
imply no_symbol -> symbol
imply mercury_symbol -> symbol
imply jupiter_symbol -> symbol
imply neptune_symbol -> symbol
imply pokeball_symbol -> symbol
imply saturn_symbol -> symbol
imply omega_symbol -> symbol
imply biohazard_symbol -> symbol
imply crescent_moon_symbol -> symbol
imply pluto_symbol -> symbol
imply onsen_symbol -> symbol
imply flamel_symbol -> symbol
imply sunagakure_symbol -> symbol
imply kirigakure_symbol -> symbol
imply xillia_symbol -> symbol
imply denpa -> symbol
imply $ -> symbol
imply yen_sign -> symbol
imply ankh -> symbol
imply ars_goetia -> symbol
imply cross -> symbol
imply fleur_de_lis -> symbol
imply hammer_and_sickle -> symbol
imply skull_and_crossbones -> symbol
imply skull_and_crossed_swords -> symbol
imply jolly_roger -> symbol
imply straw_hats_jolly_roger -> jolly_roger
imply trigram -> symbol
imply yin_yang -> symbol
imply g-clef_(suite_precure) -> symbol
imply command_spell -> symbol
imply true_rune -> symbol

imply greek_cross -> cross
imply latin_cross -> cross
imply celtic_cross -> cross
imply iron_cross -> cross
imply red_cross -> cross
imply swatstika -> cross

imply symbol-shaped_pupils -> symbol
alias symbol_in_eye -> symbol-shaped_pupils

Insignia and emblem seem to be used for the same purposes, and an emblem is a type of symbol.

The following are specific types of symbols.

The following are specific types of crosses (a symbol).

If heart-shaped pupils implicates heart and symbol-shaped pupils, then symbol-shaped pupils should implicate symbol.

Should "A physical object in the form of a cross" really be given the symbol tag? Shapes is also often used for physical objects which are no recognisable symbol, as with post #454261.

Several of the uses of symbol_in_eye are referring to cases where the symbol specifically is not the pupils like with post #2306863.

ars_goetia is often used for demons from the ars goetia, which are no more symbols than any other character is.

And does swastika (which you spelled incorrectly btw) really want to implicate cross?

No real objections to the others. If we're including all of these, though, then should the various forms of musical annotation count as symbols as well?

If so, then you could add:
musical_note -> symbol
treble_clef -> symbol
bass_clef -> symbol
sharp_sign -> symbol
flat_sign -> symbol
natural_sign -> symbol
coda_sign -> symbol
segno_sign -> symbol
accent_mark -> symbol
fermata -> symbol
tenuto -> symbol
fortissimo -> symbol
semibreve_rest -> symbol
minim_rest -> symbol
crotchet_rest -> symbol
quaver_rest -> symbol
semiquaver_rest -> symbol
demisemiquaver_rest -> symbol

(the other musical notes like crotchet etc. will want implicating to musical note as well, but that can be done separately and wants doing anyway)

Will these implications be beneficial to anyone in the long run? The symbol tag is barely used at all, and when it does get used, it's usually because the uploader couldn't think of a more precise tag (e.g., post #1633324 should be fleur de lis and post #2191585 should be hexagram). Turning symbol into an umbrella tag for dozens of other tags seems like exactly the sort of thing albert cautioned against in forum #111232.

I'm all for clearing up the relationship between emblem and insignia (and while we're at it, crest), but adding an extremely vague tag to thousands of posts simply because "X is a type of Y" seems excessive.

EDIT: As an addendum to the above, tag group:symbols already does an admirable job of grouping the various types of symbols together for convenience without all the baggage that comes with tag implications.