My best friend has excelled at this particular skill, so I figured a couple methods she's used in her hard work in training me might be useful to someone out there.
1. If you feed them, they will come.
Not an exact science, since a writer in their natural habitat won't leave their natural habitat (staring at the screen or paper), however if you feed your writer, they will make appearances. Like most wild animals, the writer must eventually eat. If you provide warm food--or even cold food, depending on the length of time since you've last seen your writer--the writer will (like a stray) come back for more. Sometimes, just shoving food in the general direction of your writer will be the most you can do, but if you wait patiently, they will again reemerge from the writing cave and seek out what they know is a good source for sustenance.
2. Let them babble.
Writing is a most solitary profession, so your writer likely spends hours if not days (and nights) with no other sound than the tap of their fingers and maybe their own voice if they pause and read things out loud. Other than, "Get down, cat!" your writer might not have spoken at all since the last time you've seen them. Although you yourself might have things to say, just let your writer babble for a bit to remove the words bursting as if from a dam just broken and they will eventually run out of steam. Allowing for this babble will mean that your writer will hear you when you speak, since the pressure from all the words unspoken has been relieved.
Your writer is babbling about some author or publisher or editor? Now they're telling you all about this person who made them mad, only for you to realize a half an hour into the conversation that they're talking about a fictional character in either their story or one they've read? Just sympathize, even if you have no clue what they're babbling about. Sometimes, your writer isn't so much looking for you to follow all that they're saying, they're simply hoping for someone to sympathize since they can't talk to anyone in the business about these things.
4. Pet frequently.
Remember, your writer is an artist at their core, no matter how businesslike they might pretend to be. As an artist, this means their temperament leads to the favorable insofar as they're great people watchers and might understand you pretty well when most people only see the surface stuff.
Conversely, this same artistic temperament means your author is constantly battling monsters known as self-doubt, insecurities, and otherwise a general surety that they're a hack. If you pet your writer, perhaps even remind them that you loved that one thing they wrote that one time, it will give your writer the steam to keep on keeping on, so to speak. One tiny nugget of belief is enough to fuel your writer for weeks, since they hoard any cheerleading comments like dragons guarding gold. When your author goes out into the world to deal with trolls, negative reviews, rejections and revisions, your breadcrumb of belief is the stuff that keeps them from turning in the writing hat and planting a nice garden instead.
5. Don't take their hermit ways personally.
Your writer can't be a writer if they're not writing. This means, sometimes? They're literally not present. They're home or in the office and writing away and it isn't that they've decided not to hang out with you...
They're not there at all. They're off slaying a dragon or otherwise living the lives of the character. They've probably not showered or eaten or even slept. So it isn't a rejection of you...they've forgotten themselves, too. It isn't personal. They do love you, but they're working. Once in a while, it is totally okay to steal your writer away from their work, since they likely won't remember to do it themselves, and will also likely thank you for the much needed break they didn't realize they required. Expect hugs and sometimes tears for this kind of rescue, but don't think it means they won't again be eaten alive by the next story or chapter.
6. Prepare to be immortalized.
Your writer will love you and cherish you so much that they'll likely give you immortality on the page. That one time you gave them a hug when they were crying? In a book. Your writer might sometimes burst into tears over fictional people or stare into space with a vague look on their face...while not remembering what you asked them to get at the store...but your writer still loves you, so you will live forever in the words they string together into stories.