I've never seen a discussion of the Constitution's "direct tax" provision, or what it specifically had to do with the 3/5 rule.
Perhaps it was considered then as a potential emergency war-time measure to quickly raise funds for national defense?
In any case it was never used, so far as I know.
The Constitution Convention debates leading to the 3/5 compromise had more to do with Northerners claiming they too wanted to count "property", so how about their livestock and furniture?
The bottom line is: slave-holders insisted they must have both Constitutional protections for slavery and representative advantages for slave-holders, while non-slave delegates were willing to settle for Union and a vague hope for slavery to eventually die out.
Taxation and representation were directly linked. Because the South controlled the central government, it controlled the taxing power. When that went away, the possibility arose that slaves might be taxed directly, and since in the late ‘50s, an able bodied male slave was a very valuable piece of property, that could hit the slaveowner pretty hard, even paying for three in five would have been a real hit. The slave states seceded because they feared a central government they could no long control.