I haven't seen many, despite their prevalence. It's always the same thing.
1) The spicy old person, like you said. "I've lived too damn long to deal with BS!" Says it like it is. Usually, they know they get away with a lot, being old.
2) Pervy old person. If this is a woman, they get away with boat loads, and it's often depicted as charming, cute, or complimentary. They're giggling about a shirtless young man or even a teenager. The pervy old man is usually portrayed more negatively, but can still be embraced as a warm character who's, overall, great (see: Uncle Iroh, although he's a very tamed version).
3) The wise, calm, "I know I know nothing" sage.
The above characters I've seen can be realistic. I've seen them all in real life. The issue isn't that they exist as characters, but that they are often the only 3 types of characters that older people get to be.
What I would like to see more of, is to see more realistic dialogue and conversations happen with / from / to seniors, since dialogue alone can heavily shape how a character is seen and executed.
It was a few years ago when I realized that often, older people are often portrayed as being flat and having lost their spark and their personality. All of that stuff is "behind them", gone with youth. It was back in the day. "Enjoy your youth, kids." 'Cause that's all there is, right? 
But that's not right. This dumb "epiphany" of mine started with the Internet actually 
. I realized that I always saw users of Internet as 30 or younger, or at least no older than 40. Especially when it came to observing how one spoke on the Internet and how they structured their sentences. Then I'd find out, as I read further, they're 70, or 80, or 90. But they came off as 20, sometimes 13. Without a voice to identify one by, everybody sounds younger on the Internet.
After that, I started paying more attention to how the elderly act when I'm out and about, and they have a lot of conversations, and behaviors, that are the same as people in their 30s and 40s, etc. Now, that doesn't mean they are the exact same. There's always the little details, like their hobbies, their favorite shows, music, etc, will likely be somewhat shaped by the time they grew up in. But not always.
When they enjoy "today's" stuff, though, others seem to think they're trying to be "hip". They aren't allowed to like new pop music or new fashions without being seen as tryhards wanting to fit in with the younger crowd, which is ridiculous. People's tastes change over time.
The same thing can be said about the language elderly folks use. All kinds of age groups are criticized, and thought of as "trying too hard" when they use buzz words, or whatever is currently the new word going around. "Swag" used to be a big one years ago. There's "BAE". Countless words that are "in", and despite us knowing language evolves, and our vocabulary also evolves as time goes on because of our exposures, we still gatekeep certain words. Elderly folks aren't "allowed" to use the vocabulary of younger generations.
But they do. Maybe not all of them. But they can, and do, and it's normal, and it's not someone trying to fit in with the younger crowds, or impress their child, nor grand child. Elderly folks are not always "behind on the times". It's ageist as heck to portray older people like that, and also very limiting.
Long story short, as with anything--gender, sex, race, nationality--portray elderly characters as people. Each group has the aforementioned details that will help ground them in reality, determined by era, environment, upbringing, and experiences lived by others for being part of a certain group, but ultimately anyone in any kind of group is still just a person. And that means not every one of them will fall into the overly-simplified, narrow box many like to put them in.
