The elders swear to fulfill their side of the bargain. What they are attempting to do is choose a judge by human means. They are attempting to force the Lord to be a (silent) witness to a purely human contract between a desperate people and an ambitious candidate. They are making it the Lord’s job to give the victory, which is something he has not yet said he would do. This appears to be another effort to manipulate the Lord.
10 And the elders of Gilead said to Jephthah, “The LORD will be witness between us, if we do not do as you say.”