The key is not to make any major improvement to the property after you have been locked in (an addition, ect).
You buy something very new, or very recently renovated just prior to turning 65 that might even be under valued on the tax rolls... then apply to lock in the current rate as soon as you turn 65 and then dont make any major improvements to the property which will reset it.
here is an article about how the freeze is affecting cities budgets:
https://www.dallasnews.com/news/news/2010/01/17/Property-tax-cap-for-seniors-puts-8031
“The key is not to make any major improvement to the property after you have been locked in (an addition, ect).”
You are only locked in on school taxes. All the other many taxes can still increase. Been there, done that.
That cap is for municipal taxes, NOT county taxes!