Short answer
Gunter is found in the Port Area. His quests, including Friendship Written in the Stars, Congregation Trouble and Rhyme and Printed, give about 10 reputation each. Congregation Trouble also brings the PR Machine, and higher Gunter reputation opens the Necronomicon technology. Before the final battle he is one of the characters whose reputation you need near 90.

The Town harbour at dusk
View full-size image ↗Official promotional screenshot · © Lazy Bear Games / tinyBuild · Official media kit · Material credits
Where Gunter is
Community guides place Gunter in the Port Area. Several story quests send you to him, including the Don Keyote quest that starts with the Donkey near the Morgue.
Quests that raise his reputation
Friendship Written in the Stars, Congregation Trouble and Rhyme and Printed are each reported to give 10 reputation.
Congregation Trouble asks you to charge a Hypno-device and hold a test sermon. Finishing it unlocks the PR Machine.
Rhyme and Printed is the poetry book quest that follows. The printing press blueprint sits in the Theology section of the Tech Tree.
Stars, Lies, and Contracts is recommended when you need the last points.

The church and graveyard in an official screenshot, where Congregation Trouble's test sermon is held. Not Gunter himself.
View full-size image ↗Official promotional screenshot · © Lazy Bear Games / tinyBuild · Official media kit · Material credits
What his reputation unlocks
Guides list 20 and 30 reputation for the two Necronomicon conversations and 40 to unlock the Necronomicon technology. Sources do not fully agree on these thresholds, so check the reputation shown in game.
Reanimation Liquid is also unlocked in the Anatomy and Alchemy section of the Tech Tree, next to Gunter's icon.
Gunter and the ending
Before the last battle, Jack, Gunter, the Nun, Herbert, Albert and Linda are each reported to need 90 reputation, or 100 if you kept the Red Eye. Their quests are said to add up to exactly 90, so skipping one can block the ending.
Sources
Related pages
Official screenshot · © Lazy Bear Games / tinyBuildAutomationGraveyard Keeper 2 PR Machine
Official screenshot · © Lazy Bear Games / tinyBuildGuidesGraveyard Keeper 2 Necronomicon
Official screenshot · © Lazy Bear Games / tinyBuildCraftingGraveyard Keeper 2 Reanimation Liquid
Official screenshot · © Lazy Bear Games / tinyBuildAutomationGraveyard Keeper 2 Hypno Device
Official artwork · © Lazy Bear Games / tinyBuildGuidesGraveyard Keeper 2 Endings
Official screenshot · © Lazy Bear Games / tinyBuildEconomyJack in Graveyard Keeper 2