Will my State Income Tax refund be taxable in 2019 if I itemize on schedule A in 2018 but do not list/deduct State income tax as a deduction?

No, if you do not take a deduction for state income taxes this year, then your refund will not be taxable next year. If you live in a state with sales tax, you could instead take the sales tax deduction.

Thank you!  Should have enough real estate tax to fill the $10K limit.