...legal reasons actually prevented him from doing so. In the state of Indiana, of which Pence served as Governor, running for more than one office on the same ballot is illegal. Pence actually tried to get a bill passed through Indiana's legislature that would allow him an exception to the law, but the bill never made it through the Indiana legislature.
After the bill allowing the legal exception failed to gain any traction, Pence officially decided to give up a shot at becoming the Republican presidential nominee in favor of running for a second gubernatorial term. However, the question still remains: Could he have secured the Republican nomination had he ran? The answer: probably not.
Pence's nomination looked very unlikely due to his extreme social conservatism, particularly in regards to gay rights and women's rights. Specifically, in 2015 Pence received a lot of criticism for his initial strong support and signing of the Religious Freedom Restoration Act, which allowed businesses in Indiana to choose whether or not to serve customers based on their religious preferences; this particularly meant that gay customers were likely to be discriminated against. Pence eventually backpedaled and signed a revised version of the bill after extreme public criticism.
Pence also has a very conservative stance on abortion rights, and directly prior to the Republican presidential primaries, he signed House Bill 1337 into law, an abortion bill "so extreme" that even many Republicans disagreed with it. Among other requirements, the bill banned abortions based on disability, sex, race, ancestry, or nationality. It also required pregnant women to view a fetal ultrasound and hear a fetal heartbeat prior to their procedure, demanded the burial or cremation of abortion fetuses by those in possession of them, and established the "crimminalization" of collecting or transferring fetal tissue. The law was eventually overturned by a federal judge, who said it would likely be found unconstitutional.
Overall, had Pence decided he even wanted to pursue the Republican presidential nomination, it is still unlikely that he would have been nominated due to his staunch support for two very extreme, publically-admonished, rights-limiting bills directly prior to the primaries.