In reviewing my database for your Rebecca Mayo who is married to Joshua Sears, I believe you have picked the wrong Rebecca Mayo.
The Rebecca Mayo you need is the one who is born 10 Oct 1713 in Barnstable County, MA and died in CT. This Rebecca Mayo's parents are John Mayo and Susanna Freeman. I got this information from a website that gave the line of descent from Richard Sears, published by the Sears Family Association. I found the website back in April 2005, so hopefully it still exists. It is as follows:http://searsr.com/richard1/pafg01.htm
I also have the Rebecca Mayo who was born 2 Dec 1710 and the daughter of Theophilus Mayo and Rebecca Smith, but I show no marriage to anyone, yet. It is true; however, that the 1710 Rebecca is a descendant of William Brewster through Patience, but her line is, starting with Patience and Thomas Prence:
Hannah Prence - Nathaniel Mayo
Thomas Mayo - Barbara Knowles
Theophilus Mayo - Rebecca Smith
The Rebecca you want has John Mayo and Susanna Freeman as her parents. I haven't followed either John or Susanna's lines back to make a link to the other Mayo's and Freeman's I also have in my records because I haven't checked too many of the Eastham, MA names in my database yet. It all takes time, but eventually I'm hoping to hit the library to review those VRs.
However, if you follow Joshua Sear's line, he too is a descendant of Patience Brewster, again via Mercy Prence - John Freeman to Thomas Freeman, Sr. - Rebecca Sparrow to Marsy/Mercy Freeman - Paul Sears to Joshua.
What information do you have that leads you to believe you need the Rebecca Mayo dau of Theophilus?