I know you replied primarily to throw a jab at my nose with the "OSU is not your rival" comment ...... but staying on topic (no offense, your comment wasn't even close to being a relevant response to my comment):
(1) If the OP's idea is going to work, every school has to be eligible for this "13th game."
(2) Some schools may have multiple options for this "13th game." For instance, WVU has all of Marshall, Virginia Tech and Pittsburgh (and arguably Maryland too) as "natural OOC rivals."
(3) However, there are some schools that do not have a "natural OOC rival" For instance -- Oregon, Oregon State, Texas Tech, Wisconsin, Minnesota. Any options we come up with for this "13th game" would be completely contrived and unnatural.
(4) If there are schools that are ineligible for this 13th game, that's unfair and we can't implement the system at all.
I'm 1 step ahead of you. All schools without a geographical or historical rival would go into "pool" of teams that can schedule games against each other and qualify for the exemption. However, there are few teams that would qualify. Lets look at the P5 schools
ACC
BC: Umass or UConn
Syr: RU, UConn, Buffalo, PSU
Pitt: PSU, WVU, RU, Temple
UVa: Md
VT: WVU, Md, ODU, Ten, Vandy, Charlotte, ECU, App St
the 4 NC schools: ECU, Charlotte, App St, ODU, South Carolina, any TN school
Clemson; SC
GT: UGa
Lou: UK
FSU: Fla
Miami: any Fla school
Big Ten:
RU: Syr, Temple, Pitt
PSU: Pitt, WVU, Syr, Temple
Md: UVa, VT
OSU: any Ohio school, have to play home and home, sorry
Mich: any Mich school, have to play home and home, sorry
MSU: ditto
Indiana and Purdue: Ball State or other MACs in neigboring states
NW: Northern Ill
Ill: Mizzou, UNI or MACs
Iowa: ISU
Neb: Oklahoma
Wisconsin: Northern Ill or go into pool of teams without a rival
Minnesota: pool of teams without a rival
SEC:
Ten: Memphis, MTSU, VT
UK: Lou
SC: Clemson
UF: FSU
Mizzou: KU, KST, Ill
UGa: GT
Vandy: MTSU, Memphis
Alabama: Troy, South Alabama, UAB, have to play home and home, sorry
Auburn: ditto
Ole MIss: Southern Miss, Memphis or other American/CUSA/Sun Belt schools in neighboring states
Miss St: Southern Miss or other CUSA/American.Sun Belt schools in neighboring states
LSU: Tulane, La Tech, ULL, or ULM
Ark: Ark Stat, Memphis or other CUSA/AMerican/Sun Belt schools in neighboring states
A&M: Texas
Big 12:
WVU: Pitt, PSU, Md, VT, Marshall
ISU: Iowa
Kansas: Mizzou, Colorado, Col St, AFA
KST: Mizzou, Colorado, Col St, AFA
OU: Neb
OKST: Tulsa or Texas CUSA/AMerican/SB schools
Texas: A&M
TT, TCU, Baylor: UTSA, UNT, UTEP, Houston, SMU, Rice, Texas State
Pac 12:
Arizona, ASU: NM, NM State, Nevada, UNLV
UCLA, USC, Stan, Cal - SDSU, SJSU, Fresno, UNLV, Nevada
Or, ORST - Boise, Idaho, Fresno, SDSU, SJSU, Fresno
Wash, Wash St - Boise, Idaho
There you have it. Every P5 team has a geographical or historical rival except Minnesota and Wisconsin (if you dont count UNI a mere 100 miles away). Perhaps they can be given an exception to schedule a 13th game.
The point of this is to promote college football. There would also have to be a panel created to review exemption requests. Example: PSU wants to use their exemption to schedule Temple, an in-state team they have played many times but have only lost to once. However, Pitt wants to schedule PSU as their exempted game. The panel would tell PSU that they can only use their exemption on Temple, Syr, or WVU in the years that Pitt is not available since that is the kind of rivarly that is trying to be protected.
Same thing goes for Texas & A&M. Texas cant go out and schedule UTSA or UNT if A&M has an open spot for them.
WIth the 13 game schedule, you get:
9 conference games
1 1-AA game
1 G5 game
1 P5 game
1 Exempted rivalry
Also, with my rule, it should be noted that there the 13th game does not have to be played. If PSU doesnt want to play Pitt or the Big Ten schools dont want to play MACs, then they dont have to. They'll just continue their 12 game schedule. But if they want the extra revenue, they can play the 13th game.