What do you mean by Senior Tax Credit?  The Federal  Credit for the Elderly or Disabled, or rather some state credit?

To determine if you can claim the credit, you must consider two income limits. The first is the amount of your adjusted gross income (AGI).  Adjusted Gross Income (Form 1040 or 1040-SR, line 11).  You do not subtract the Standard Deduction (line 12) from that.   The second limit is the amount of nontaxable social security and other nontaxable pensions, annuities, or disability income you received. 

Looking at the tax form may help, as Gross Income v. AGI v. Taxable Income can get confusing.

2020 Form 1040-SR (irs.gov)

Thanks for quick answer. Yes, I meant "Federal  Credit for the Elderly or Disabled".
Lets assume an AGI of  $19,999 (line 11 on 1040) and no other income (e.g. no nontaxable social security and other nontaxable pensions, annuities, or disability income).

The Standard Deduction is $26,100 (line 12 on 1040).
The Taxable Income is then $0 on Line 15  (Line 11 - Line 12).

Thus, the Tax Liability is $0,  and no credit is allowed.

You are correct.  This tax credit can wipe out some, if not all, of your tax liability if you end up owing the IRS. This is especially helpful if you have self-employment income, on which extra taxes are due, or some other tax liability.  As the years have gone by, the Standard Deductions have gone up, but not the income limits, so some folks like you (one over 65, and one under 65) get caught in a Catch 22.  But it does work for Singles over 65, and Married Couples where both are over 65.

Self-employment income would just increase the AGI and not make a difference.  Since the max AGI, for the credit is $19,999.99, and the standard deduction is $26,100, the taxable income will always be $0 and no credit allowed.

It seems that IRS needs to correct the Income Limits for married couples with one spouse less than 65. Without the correction, the "Federal  Credit for the Elderly" will be meaningless for those couples.