Linda Bartoshuk’s The Biological Basis of Food Perception and Acceptance (Food Quality and Preference 4, 21–32, 1993) gives a detailed historical account of the tongue map that is mostly accessible to laypeople. I will only quote the important parts here (boldface mine):

The tongue map with ‘sweet’ on the tip, ‘bitter’ on the back, etc., dates back to the PhD thesis of Hänig […] However, it is important to note that Hänig did not plot the actual sensitivity values. Instead he plotted rather impressionistic curves meant to show the rate of change from one locus to the next. […] Saltiness was perceived approximately equally on all loci so Hänig did not include it in his figure. […]

Edwin Boring […] discussed Hänig’s thesis […] in 1942. Boring did not reproduce Hänig’s summary sketch but rather calculated the actual sensitivities by taking the reciprocals of the average thresholds given in Hänig’s tables. Then for each stimulus, Boring divided each of the sensitivity values by the maximum sensitivity achieved for that stimulus […]. Boring then smoothed the curves a bit and labeled the ordinate ‘sensitivity’ without providing actual values. […]

On Boring’s figure, there is no way to tell how meaningful the sizes of the variations are on the ordinate. Boring’s graph led other authors to conclude that there was virtually no sensation at the loci where the curves showed a minimum and that there was maximum sensation where the curves showed a maximum and so we have the familiar tongue maps […]. Even with the ordinate labeled […], the meaning can be confusing. Consider an example from the sweet data. At H [the base of the tongue], the sweet sensitivity was 0·3 while at A [the tip of the tongue] it was 1. This looks like an impressive difference until we recall what the sensitivity scores mean. In fact, they simply mean that at H the threshold was about one-third what it was at A. To see what this reflects, look at Fig. 5 [which shows the distribution of threshold across subjects, which spreads across several orders of magnitude]. […] Note that this is a relatively small change.

Collings reexamined the threshold variation in 1974. Her results differed from those of Hänig in some regards […]; however, in one very important particular Collings and Hänig agreed. There were variations in taste threshold around the perimeter of the tongue but those variations were small. Essentially, sweetness, bitterness, saltiness, and sourness can all be perceived on all loci where there are taste receptors.