SSD always mounts as read-only on Mac OS Mojave
I wrote a bash script that I execute every time after inserting the drive
function mountTimeMachineDriveRWSANDISK1TBSSD() {
    diskutil mount /dev/disk2s2 # disk2s2 is from the output of diskutil list
    sudo mount -v -u -w /dev/disk2s2 /Volumes/SANDISK1TB # disk2s2 is from the output of diskutil list
    sudo chown myuser /Volumes/SANDISK1TB
    sudo chgrp mygroup /Volumes/SANDISK1TB
}

Now the disk is writable by the current user. Time machine can backup to this disk too.