Ok, due to some "alternate" views on tightening wire wheels, I actually spent time researching the issue.
The Austin Healey 3000 Mark III Driver's Handbook calls it a "knock-on" and says:
"Tighten the hub cap with a mallet."
The Austin Healey Workshop Manual says:
"When the car is new:After the first long run or after 50 miles of short runs, jack up the wheels and hammer the nuts to make sure they are tight. Always jack up the wheel before using the hammer."
The Haynes Austin Healey 100/6 & 3000 Owner's Workshop Manual says:
"Monthly or every 1000 miles check 'knock-on' wheel caps for tightness".
Dayton's web site says:
Tighten Caps
While car is still on jacks run the knock-off caps up tight. Two-eared and 3-eared caps must be tightened with a Dayton WireWheel lead hammer. Octagon,
Dome, Diamond, and OTD caps must be tighten with the appropriate wrench and lead hammer. Wrench tightening alone is not sufficient.
Test
Spin wheels by hand to make sure there is no rubbing against brake calipers. Also, rock wheel assembly to verify that the knock-off cap has seated completely in the wheel. No looseness should be noticeable.
Retighten Caps
Lower the car and hammer the caps until there is no movement under the hardest blow of the hammer. After the car has been run 25 miles, be sure to re-check
the knock-off cap for tightness. The wheels seat themselves on the adapters after the initial run-in and knock-off caps can be tightened further. THIS IS
IMPORTANT. Knock-off caps must be very tight to prevent wear of the drive teeth. Continue to tighten knock-off caps every 100 miles for the first 500 miles.
Then check tightness every few weeks. WIRE WHEELS should always be checked for tightness of knock-off caps regularly.
https://www.daytonwirewheels.com/pdf/installationinstructionsfork-o.pdf
I hope this provides ample authority and instruction for how and how often to tighten your knock-ons. PLEASE DO NOT THINK YOUR KNOCK-ONS TIGHTEN THEMSELVES. Your life is at risk.