Not sure what 'spiffy' means - thinking it means good? So if he did it well for his last owner, chances are he's been taught how to, at least basically. It also sounds like you're getting what you ask for a step or 2, which is a great start. You just need to reinforce it - let him know he's done Right - rather than try to drag more from him.
I think the above is good advice, but will give my take on what is effective. Firstly I'd make sure he's really soft & responsive to direct pressure on the ground. Then I tend to teach basic ridden rein cues from on the ground first too. Eg. Stand beside him, holding both reins at his wither, so you can cue approx the same as when riding.
When you first start riding, it may be best to have someone leading him to begin with, to back up your requests if he doesn't understand, because if he won't back up, chances are his slowing & stopping isn't great either, which can be dangerous. I'd also make certain it's not a saddlefit or other discomfort issue, as trying to just train something into them that they can't or won't do for physical reasons will only make matters worse.
I want my horses to ultimately follow a 'feel' and my subtle seat cues, so that is where I begin my 'ask', building the degree of 'request' or pressure to do it gradually but consistently, so they learn what to respond to, to avoid actual pressure. Therefore I'd start asking by sort of dropping in the saddle, as in stopping/slowing, but without dropping my energy. If/when he doesn't get that, I'd back it up by raising my hands, gradually taking the slack out & getting firmer with the pressure. If I were by myself, I'd increase the pressure. Gradually, to make it uncomfortable for him, but hold there, not try to pull or increase to a painful level. If I had a helper, I'd get as far as taking the slack out & that's where they'd start asking from the ground to back it up.
Most importantly, you want to make the Right things easy & reinforce them. Think about him being in preschool - you're wanting to teach counting from one to ten, not expect addition yet, let alone algebra. You need to reward his tries & start with the very basics. Start at the level you think he can give & build gradually from there. Even if you have to start by reinforcing him for just softening & shifting his weight back, get him reliable & confident about that before asking for more, in baby steps. I like to reinforce them both negatively - by instantly removing the pressure - and positively - reward with something Good, be that a rub or scratch if he likes that, or food treat or such.