Here is some contextual information I was able to find (not a full answer--I hope the bounty will attract one):
What sources say about the dative ending
The dative ending -ū is well attested with non-neuter nouns, not just with neuter nouns:
An alternative dative ending -ū, which is normal for neuters like cornū 'to the horn', genū 'to the knee', often appears in masculine and feminine forms as well: cf. ūsū 'to the use' (Plautus), vestītū 'to the attire' (Terence), adspectū 'to the sight' (Vergil). It seems to be the result of the strong mutual influence between the ablative and dative, apparent in all plurals, in o-stems, and in some forms of consonantal stems. It is also common in poetry, where metrical requirements often demand a reduction of the diphthong to -ū. Alternatively, it may be an old endingless locative such as *-ō̆u.
(The Foundations of Latin, by Philip Baldi, p. 331)
And it looks like on the other hand, some sources may give -uī as a possible dative ending for neuter nouns, not just non-neuter nouns
Lewis and Short mention a dative singular form genui although I'm not sure whether they would group it with the nominative singular form genu or the nominative singular form genus.
András Cser denies the relevance of gender to the -uī/-ū variation in the dative, saying
As a point of variation the dative of u-stems can also be identical to the ablative instead of taking the -ī suffix.184
- Contrary to what Spaelti (2004:133) claims, the u-stem dative without the -ī is not more typical of neuters than of masculines and feminines.
(Aspects of the Phonology and Morphology of Classical Latin, 2016, p. 130)
If this is true, it might only be possible to answer the slightly different question of "how did books about Latin come to show the neuter fourth-declension dative singular as different from the non-neuter ending"?
Fourth-declension neuter nouns are a very small category containing no words that are particularly frequent in the dative singular
As far as I know there are fewer than ten fourth-declension neuter nouns. It therefore seems plausible that you could try to compile a complete list of all attested usages of any fourth-declension neuter noun in the dative singular in ancient sources. I haven't done this work or found an existing list, though.
Not sure if it's relevant, but neuter nouns in the fourth-declension can also have a genitive singular in -u (-ū) instead of -ūs. I'm not sure how far back this goes; Neo-latin Studies: Significance and Prospects, by Hans Helander, says neuter genitive -ū shows up in Charisius (fl. 4th century AD) (page 30).
Zumpt 1855 says
Formerly it was believed that the neuters in u were indeclinable in the singular, but recent investigations (especially those of Freund, in an Appendix to the preface to his Latin Dictionary) compel us to give up this opinion, especially with regard to the genitive; for it is only in late technical writers that we find, e.g., cornu cervinum and cornu bubulum making the genitive without any termination of the first word: cornucervini, cornububuli.