What are all the implications of paying your property taxes when they have gone into default mode or six months late?

In my state (IL) if you do not pay your property taxes the year they are due, later that fall or following spring your property goes to tax sale auction. There is still a 2 year redemption period. Whoever buys your tax lien is obligated to tell you when certain deadlines are. If you pay the tax, penalty, and interest to the county during that 2 year redemption period, that goes to whoever bought your tax lien and you get to keep your property. If you do not pay it in that 2 years, whoever bought the tax lien gets your property.

But that varies by state and possibly by county, so you should go to your county treasurer or assessor website to find out more details. Some states go 5 years before you lose your property. But do not assume anything unless you find out for certain in your location.

Also if you have a home loan and do not pay your property taxes on time, that can put your loan in default.

Common sense should tell you that the sooner you pay overdue taxes, the better.

What the hell does that even mean?

Pay your damn taxes

there will be an automatic 10% penalty

You can deduct it when you pay it.