What would mandatory gun ownership have to do with anything I've said?
It was a reference to the fact that the ACA penalty was held constitutional as a tax not a penalty. But that's okay.
Anyhow Insurance such as car insurance is only mandatory for those engaging in a certain act or otherwise by contract in the example of homeowners insurance. Thus, I can own a car and not buy car insurance as long as I do not drive that car. Or I can own a home and not buy homeowners insurance unless I have agreed to purchase such by contract. Health insurance is a little different. With health insurance now, one can still not purchase health insurance, however, there is a consequence i.e. you pay a higher tax come income tax time.
Now, the problem is that requiring an on-going tax on a specific class of people reeks of equal protection violations. ACA doesn't have to worry about this because that tax applies to everyone equally, thus anyone who chooses to forgo the purchase of health insurance pays the tax. If we change the statement to say any gun owner who doesn't acquire insurance must pay a tax, then we see that we are now targeting a specific class of people with a tax. Sales taxes are different they are a one time shot that you pay at purchase. It is not a law that only attacks a specific class of people either. Sales tax goes to everyone in the states that have such a tax. Some items are exempt, but we see it touch everything else.
Any effort to tax a specific class of people will still be subject to the rational basis test of the fourteenth amendment. So, as I said before, depending on who implements the law, how it is implemented and why it is implemented will determine whether the law is constitutional. On its face, without other facts this suggestion would be unconstitutional because it does not pass the rational basis test.