So here's the context. Madhav stared at the girl driving beside him, not for the first time. She was probably about his age, with dark brown hair cut pretty short, up to her shoulders. “Again, I can’t thank you enough for this. Thank you so much.” She looked at him, and smiled. The smile seemed to light up her already pretty face. There was a twinkle in her eye, and for some reason, Madhav got the feeling that that twinkle was always there. “I already told you, I’m going the same way. There’s no need to thank me as profusely as all that.” With a start, she jerked her eyes back on to the road and sighed. She was obviously a very bad driver. “So. What do you think happened to your car?” she said, her eyes still on the road. “Don’t know. Something to do with the radiator fan, or the break fluid, or the carburetor, I suppose. Or maybe the gear transmission is messed up. I have no idea. That car is almost six years old. That’s menopause in cars, no? For all I know, there may be a giraffe peeing into the fuel tank.” She laughed. “I see. You obviously know a lot about cars.” “Careful with your sarcasm. It’s dripping on me a little.” She laughed a little harder that time. She liked that, did she? He could come to love this girl. He shook his head in *blank*. I can't, for the life of me, think of a word to fit. Any ideas? I'm looking for something that will explain a cynical attitude towards his own thoughts, a slight sense of self-pity, and amusement. I know this is really desperate, but I am, for the lack of a better word, desperate. Thank you!
Just delete the last sentence. You've done a good job of communicating the mood in the first few paragraphs. We don't need the "word" to know what you mean.
I'd rewrite the last sentence something like this, taking a bit of a leap of logic with what I think you're aiming at with Madhav's thinking: She laughed a little harder that time. So she liked that, did she? He thought that he could come to love this girl, but then caught himself immediately and gave his head an almost imperceptible shake. He didn't want to delude himself with such positive thoughts again.
The thing is, I don't get "self-depricating" from the paragraph. It is not clear from what you have written and I was quite surprised that was his sentiment (probably because I don't know the character). But I still think that the word you are looking for is probably not there because it would require an explanation instead. Something like: I usually try to avoid putting my words in another writer's mouth because it never works, and by no means am I suggesting you should use my example, I only wanted to illustrate that perhaps you should show rather than tell this emotion you are thinking of.
Another word that may need fixing: it's "brake" fluid, not "break". I've made the similar mistakes many times, so don't feel bad.
Exasperation? Bemusement? There are a lot of potential words to fit that blank. On a different note, I don't really see how she's a bad driver. Obvious how? Jerking her eyes to the road and sighing doesn't give me the impression that she's a bad driver. And it seems like a random action inserted between dialogue. Why were her eyes off the road to begin with? Some clarification would be nice.
vacillation World English Dictionary vacillate (ˈvæsɪˌleɪt) — vb 1. to fluctuate in one's opinions; be indecisive 2. to sway from side to side physically; totter or waver