Can a homeowner without a Section 608 EPA license legally connect his own gauges to his own air conditioner if the unit uses 410a refrigerant?
The law against "unlicensed" refrigerant handlers (whatever that means) does not specify any penalties, it just says it is "prohibited", so from a legal standpoint it is an unenforceable law. In order for a law to be prosecuted it must have a penalty specified, otherwise it is moot in court. For this reason, noone has ever been indicted for violating this so-called "prohibition".

In general, only companies are sued by the EPA for refrigerant issues, not individuals, with the exception of refrigerant "smugglers" who are indicted on trade laws, not Clean Air Act violations. In the last 10 years only one (individual not company) person has ever been domestically convicted of a Freon-related violation. That was a guy who was brazenly selling Freon on Craigslist. Even in this case, he was convicted of filing false documents with the Feds, not of actually selling the Freon.

No individual householder has ever been criminally charged for maintaining, charging or otherwise working with refrigerants, illegal or otherwise, in their own home or business.