I am 63 and my wife is 64. I will retire next month and start drawing on SSA (reduced ~$3000). If my wife decides to start drawing also (~$500) will she be eligible for the 50% spousal benefit when she reaches FRA and will it be based on my FRA amount or my reduced amount.
Your wife couldn't file for her own benefits without also being deemed to file for spousal benefits. And, if she starts drawing both benefits before full retirement age (FRA) they'll both be reduced for age.
Your wife's unreduced spousal rate would be based on 50% of your primary insurance amount (PIA), not your reduced benefit rate. A person's PIA is the amount they'd receive if they start drawing their Social Security retirement benefits at FRA. However, your wife can only be paid essentially the higher of her own benefit rate or her spousal rate, not both.
For example, say Jan and her husband file for their benefits this month at age 64 and 63, respectively. Jan's PIA is $800 and her husband's PIA is $2000. Jan's husband's reduced age 63 rate would be $1566, but that's irrelevant to the calculation of Jan's spousal rate. Jan's unreduced spousal rate would be calculated by subtracting her PIA from 50% of her husband's PIA, which is $200 in her case (i.e. $2000/2 - $800). However, since Jan is filing at age 64 her own benefit amount is reduced to $684 and her spousal benefit is reduced to $163, giving Jan a combined reduced benefit rate of $847.
By the way, if you start drawing at age 63 your reduced benefit rate won't be as much as $3000. That's significantly more than the current maximum possible monthly rate for someone filing at age 63. You and your wife should strongly consider using our software (https://maximizemysocialsecurity.com/purchase) to find out your correct benefit rates and to determine your best strategy for claiming your benefits.