Does the paperwork you have regarding the widow's pension have any information regarding the unit, or even the year his widow applied for the pension? A brief search of the Civil War pension index turns up only one Willis H. Mays, but he was in an Iowa Regiment.
While it is not impossible that your ancestor served in the Civil War, he would have been about 65 years old at the time --- which is pretty old for active campaigning. He could have joined a short term Militia unit, however.
There is a Willis Mays who served in a Virginia Regiment during the War of 1812 --- Is it possible that this was your ancestor? He would have been about 17 years old at that time. The information is:
Willis Mays 90 Regiment (March - August 1813) Virginia Militia