Neat idea.
I'd have an irl yandere story and a story based on another one to write down, but I'm not motivated to do so and I currently do not have time ...
Plus, I was wanting to hear some input from Yanderes themselves, on how I should go about a story with this archetype.
There's really too much needed context to give much general advice. Caricatures work much better in comedy than drama. Yandere as main villain needs a different approach than yandere as hero, or yandere as deuteragonist, or yandere as minor character.
As far as general advice goes:
1) Yandere are people too. In particular, a yandere has probably had some interests prior to his/her love interest, unless they're childhood friends. May include other love interests (dead, fled, or otherwise), but other stuff too. This is less relevant for a comedic caricature, though, or to some extent a minor character.
2) Yandere as hero is rare in recent published works, especially Western ones (as opposed to yandere as deuteragonist, which is common enough). There are reasons for this, but it's potentially unclaimed territory. To a lesser extent, plot-irrelevant yandere (i.e. not the basis of a story arc, just there in the background) is also not that common.
I’m going to build on what magic9mushroom says. I believe that to write a Yandere character, you should start with a person like any of us. I think one of the strengths of Yandere characters lies in how you reveal their complexity, and that depends on the time you take to narrate it.
I also write things from time to time and take the time to think about what is happening and what methods I have to present and time these events. After I have a draft, I read it and ask myself, "Is it worth it as a narrator to say 'this'?" "Can I do the same thing but in a different way?" From there, I look for what I like more in my writing and keep moving forward.
I also try to research with short stories, novels, or even Wattpads to see which elements I like and analyze them to see if I can reuse any resources.
I'd love to read your stories.
I've got a few ideas for games I'd really like to publish some day with yandere protagonists or deuteragonists (I'm currently focused on more mainstream games, but maybe in the next few years I'll ship one of the Yandere-related games.) So I think about the role they can play in stories and the evocative impact they can have quite a bit.
ᴛʜɪꜱ ɪꜱ ʀᴀᴛʜᴇʀ ʟᴀᴛᴇ, ᴀɴᴅ ɪ'ᴍ ɴᴏᴛ ʀᴇᴀʟʟʏ ᴀ ᴡʀɪᴛᴇʀ(ᴍᴏʀᴇ ᴏꜰ ᴀ ʜᴏʙʙʏɪꜱᴛ ᴡʀɪᴛᴇʀ), ʙᴜᴛ ɪ ꜰɪɢᴜʀᴇᴅ ɪ ᴄᴏᴜʟᴅ ᴄᴏɴᴛʀɪʙᴜᴛᴇ ᴛᴏ ᴛʜɪꜱ ᴛʜʀᴇᴀᴅ. ᴇᴠᴇʀʏᴏɴᴇ ᴇʟꜱᴇ ʜᴀꜱ ᴀʟʀᴇᴀᴅʏ ꜱᴛᴀᴛᴇᴅ ᴛʜᴇɪʀ ᴘɪᴇᴄᴇ ᴡɪᴛʜ ʜᴏᴡ ᴛᴏ ɢᴏ ᴀʙᴏᴜᴛ ᴛʜᴇ ʏᴀɴᴅᴇʀᴇ ᴄʜᴀʀᴀᴄᴛᴇʀ ᴀʀᴄʜᴇᴛʏᴘᴇ, ꜱᴏ ɪ ᴡᴏɴ'ᴛ ɢᴇᴛ ɪɴᴛᴏ ᴛʜᴀᴛ.
ɪɴꜱᴛᴇᴀᴅ, ɪ ᴡᴀɴᴛ ᴛᴏ ᴘᴏɪɴᴛ ᴏᴜᴛ ᴛʜᴇ ᴍᴀɪɴ ᴄᴏɴꜰʟɪᴄᴛꜱ ᴍᴏꜱᴛ ʏᴀɴᴅᴇʀᴇ ꜱᴛᴏʀɪᴇꜱ ꜰᴏʟʟᴏᴡ.
- ʏᴀɴᴅᴇʀᴇ ᴠꜱ. ᴛʜᴇ ᴍᴄ (ᴘᴇʀꜱᴏɴ ᴠꜱ. ᴘᴇʀꜱᴏɴ)
- ʏᴀɴᴅᴇʀᴇ ᴠꜱ. ᴀ ʀɪᴠᴀʟ (ᴘᴇʀꜱᴏɴ ᴠꜱ. ᴘᴇʀꜱᴏɴ)
- ʏᴀɴᴅᴇʀᴇ ᴠꜱ. ꜱᴏᴄɪᴇᴛʏ (ᴘᴇʀꜱᴏɴ ᴠꜱ. ꜱᴏᴄɪᴇᴛʏ)
ɪ ᴛʜɪɴᴋ ɪᴛ'ʟʟ ʙᴇ ɪɴᴛᴇʀᴇꜱᴛɪɴɢ ᴛᴏ ꜱᴇᴇ ᴍᴏʀᴇ ʏᴀɴᴅᴇʀᴇ ꜱᴛᴏʀɪᴇꜱ ᴛʜᴀᴛ ꜰᴏʟʟᴏᴡ ᴀ ᴅɪꜰꜰᴇʀᴇɴᴛ ꜰᴏʀᴍᴀᴛ.
ꜰᴏʀ ᴇxᴀᴍᴘʟᴇ...
♥ ʏᴀɴᴅᴇʀᴇ ᴠꜱ ꜰᴀᴛᴇ (ᴘᴇʀʜᴀᴘꜱ ᴀɢᴀɪɴꜱᴛ ᴛʜᴇɪʀ ᴏᴡɴ ꜰᴀᴛᴇ ᴏʀ ᴛʜᴇɪʀ ᴅᴀʀʟɪɴɢꜱ? ᴏʀ ᴀɢᴀɪɴꜱᴛ "ɢᴏᴅ" ᴊᴜꜱᴛ ᴛᴏ ʙᴇ ᴡɪᴛʜ ᴅᴀʀʟɪɴɢ?)
♥ ʏᴀɴᴅᴇʀᴇ ᴠꜱ ᴛʜᴇ ᴜɴᴋɴᴏᴡɴ (ᴇx.: ʏᴀɴᴅᴇʀᴇ ɢᴏɪɴɢ ᴛʜʀᴏᴜɢʜ ᴜɴᴄʜᴀʀᴛᴇᴅ ᴡᴀᴛᴇʀꜱ ᴛᴏ ꜰɪɴᴅ ᴛʜᴇɪʀ ᴅᴀʀʟɪɴɢ ᴏʀ ꜰᴀᴄɪɴɢ ᴀ ᴜɴᴋɴᴏᴡɴ ᴏʙꜱᴛᴀᴄʟᴇ)
♥ ʏᴀɴᴅᴇʀᴇ ᴠꜱ ꜱᴇʟꜰ(ᴛʜᴇꜱᴇ ᴀʀᴇ ᴍᴏʀᴇ ᴄᴏᴍᴍᴏɴ ɪɴ ʀᴇᴅᴇᴇᴍᴇᴅ/ᴇɴʟɪɢʜᴛᴇɴᴇᴅ ʏᴀɴᴅᴇʀᴇꜱ ᴡʜɪᴄʜ ɪ'ᴅ ʟᴏᴠᴇ ᴛᴏ ʀᴇᴀᴅ ᴀʙᴏᴜᴛ ᴍᴏʀᴇ ꜱɪɴᴄᴇ ᴛʜᴇʏ'ʀᴇ ʀᴀʀᴇ)
ᴏꜰ ᴄᴏᴜʀꜱᴇ, ʏᴏᴜ ᴀʀᴇ ꜰʀᴇᴇ ᴛᴏ ᴡʀɪᴛᴇ ᴡʜᴀᴛ ʏᴏᴜ ᴡᴀɴᴛ ᴛᴏ ᴡʀɪᴛᴇ! ɪ'ᴍ ᴊᴜꜱᴛ ᴛʜʀᴏᴡɪɴɢ ꜱᴏᴍᴇ ꜱᴜɢɢᴇꜱᴛɪᴏɴꜱ. ɪ'ᴅ ʙᴇ ɪɴᴛᴇʀᴇꜱᴛᴇᴅ ɪɴ ʀᴇᴀᴅɪɴɢ ʏᴏᴜʀ ꜱᴛᴏʀɪᴇꜱ ɪꜰ ʏᴏᴜ ᴇᴠᴇʀ ᴘᴜʙʟɪꜱʜ ᴛʜᴇᴍ ᴏɴᴇ ᴅᴀʏ.