One signature per sending address
If you use the Send mail as feature to send from more than one address, each address gets its own signature. Use the drop-down above the signature box to pick the address before you paste.
Gmail keeps signatures in the General tab of its full settings screen, not in the quick settings panel that opens when you click the gear. Set it once in a browser on a computer. The steps below take about a minute, and the one people miss is the last one.
Make one first. The generator is free, needs no account, and gives you something to paste before you open your settings.
If you use the Send mail as feature to send from more than one address, each address gets its own signature. Use the drop-down above the signature box to pick the address before you paste.
Google caps a Gmail signature at 10,000 characters and counts the image against that limit. If Gmail refuses to save, the usual cause is a large image; resize it and try again.
If you cannot format the signature and the words Plain Text appear above the signature box, turn plain text mode off before editing. In plain text mode Gmail strips the layout and you get an unstyled block.
Every recipient of every email fetches your logo and photo from the address they live at. A Google Drive image has to be shared publicly to work, and deleting the file stops the image appearing in signatures that already went out.
If you set the defaults to none, you can still add the signature to a single message: at the bottom of the compose window, click Insert signature and pick it.
The Gmail apps for Android and iPhone keep their own signature setting and Google documents them on their own pages. Set this one on a computer first.