Worth bearing in mind, when thinking about all of this, is who wants the FBI to investigate and who doesn't want the FBI to investigate. Ford does. Trump Does not.
Now think about which position each is likely to take if they think/know a) that Ford is lying or b) they think/know that Ford is telling the truth.
Trump could make the FBI investigate, but will not and has give two different, false reasons to justify that.
I thought the same thing, that her willingness/eagerness to have a full investigation bolsters her case, and casts doubt on the Republican side, but on further reflection, I'm not so sure.
Let's consider the three possibilities you brought up.
1) She's telling the truth.
2) She thinks she's telling the truth, but is mistaken due to some combination of mistaken identification, bad memory, delusion.
3) She's lying. (i.e. she is knowingly providing false information.)
In case 1) she would want an FBI investigation because she knows there are other witnesses or people with knowledge about the situation who are reluctant to come forward, but the investigation might cajole them into coming forward and providing the needed corroboration.
From her perspective, case 2 is the same as case 1.
What about case 3? It's tempting to say that if she were lying she would not want an investigation because it might bring forward people who could contradict her story. However, that's not really how liars think. Liars make up lies because they think they can get away with the lies. If you look at her story, there's very little that an investigation could uncover (she thinks) that could disprove her story. She has provided very little data that can be confirmed. She has named only a few names, and they have clear incentives to lie. If she were lying, she would be pretty sure that an investigation would turn up nothing, in which case it's still her word against Judge and Kavanaugh, with everyone else just not being able to remember. Meanwhile, the willingness to be investigated looks good to the "jury" of public opinion.
What about from his perspective?
Case 1. If she's telling the truth, he definitely does not want an investigation.
Case 2. If her story is not true, then it would be tempting to say that he ought to want an investigation. However, the investigation would have to go into a lot of things that happened back in the days when he was in the 100 keg club, or something similar. I remember those days myself. (Well, most of them anyway.) Even if they don't prove the story is true, or indeed even if they somehow manage to disprove it, goodness knows what else they might uncover. It might not be criminal, or anything like that, but it could be quite embarrassing. Nothing can be gained from his perspective, and a fair amount could be lost, even if her allegations are false.
Case 3. From his perspective, same as case 2.
So, even if her story is not true, she gains, or thinks she would gain, from an investigation. Even if her story is not true, Kavanaugh still has a lot to lose from an investigation.
And on top of that, it would just take some time. If it keeps him off the court until after the first Monday in October, that still means he misses the chance to be part of any cases at the beginning of the term.
So, on further reflection, their attitude toward an FBI investigation really doesn't tell us much. Both of them have incentives to take the positions they have taken, regardless of whose version of events is true.