We measure the metallicities of 374 red giant branch (RGB) stars in the isolated, quenched dwarf galaxy Tucana using Hubble Space Telescope (HST) narrow-band (F395N) Calcium H & K (CaHK) imaging. Our sample is a factor of similar to 7 similar to 7 larger than what is published. Our main findings are: (i) A global metallicity distribution function (MDF) with <[Fe/H]>=-1.55(-0.04)(+0.04) and( sigma)[Fe/H]= =0.54(-0.03)(+)(0.03) (ii) A metallicity gradient of -0.54 +/- 0.07-0.54 +/- 0.07 dex R-e(-1) (-2.1 +/- 0.3- dex kpc(-1)) over the extent of our imaging (similar to 2.5R(e)), which is steeper than literature measurements. Our finding is consistent with predicted gradients from the publicly-available FIRE-2 simulations, in which bursty star formation creates stellar population gradients and dark matter cores; (iii) Tucana's bifurcated RGB has distinct metallicities: a blue RGB with <[Fe/H]>=-1.78(-0.06)(+0.06)<[Fe/H]>=-1.78(-0.06)(+0.06) and sigma([Fe/H])=0.44(-0.06)(+0.07 )and a red RGB with <[Fe/H]> = -1.08(-0.07)(+0.07 and alpha)[Fe/H] 0.42 +/- 0.06(iv) At fixed stellar mass, Tucana is more MR than MW satellites by similar to 0.4, but its blue RGB is chemically comparable to the satellites. Tucana's MDF appears consistent with star-forming isolated dwarfs, though MDFs of the latter are not as well-populated; (v) similar to 2 similar to 2% of Tucana's stars have [Fe/H]<-3[Fe/H]<-3 and 20% [Fe/H]>-1[Fe/H]>-1. We provide a catalog for community spectroscopic follow-up.