Mouse movement stops after switching to text VT and back to X

My Dell Inspiron 6400 laptop has a Synaptics touchpad. If I'm using xserver-xorg-input-synaptics and I use Control-Alt-Fkey or sudo chvt to switch to a text virtual console and then switch back to X, the mouse stops moving via the touchpad. The touchpad seems totally ignored, and I can't tap to click either. However, the two physical mouse buttons located below the touchpad continue to work properly. Also, sudo evtest shows that touchpad events are still delivered by the kernel.

If I apt purge xserver-xorg-input-synaptics and use the touchpad like a generic mouse, this does not happen. If I do that and then install xserver-xorg-input-libinput, using the touchpad via libinput, this also does not happen.

ProblemType: Bug
DistroRelease: Ubuntu 20.10
Package: xserver-xorg-input-synaptics 1.9.1-1ubuntu3
ProcVersionSignature: Ubuntu 5.8.0-31.33-generic 5.8.17
Uname: Linux 5.8.0-31-generic x86_64
NonfreeKernelModules: wl
ApportVersion: 2.20.11-0ubuntu50.2
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: XFCE
Date: Wed Dec 9 11:32:34 2020
DistUpgraded: 2020-10-21 19:30:44,581 DEBUG Running PostInstallScript: './xorg_fix_proprietary.py'
DistroCodename: groovy
DistroVariant: ubuntu
InstallationDate: Installed on 2012-01-19 (3247 days ago)
InstallationMedia: Xubuntu 11.10 "Oneiric Ocelot" - Release amd64 (20111012)
Lsusb:
 Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
 Bus 005 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
 Bus 004 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
 Bus 003 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
 Bus 002 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Lsusb-t:
 /: Bus 05.Port 1: Dev 1, Class=root_hub, Driver=uhci_hcd/2p, 12M
 /: Bus 04.Port 1: Dev 1, Class=root_hub, Driver=uhci_hcd/2p, 12M
 /: Bus 03.Port 1: Dev 1, Class=root_hub, Driver=uhci_hcd/2p, 12M
 /: Bus 02.Port 1: Dev 1, Class=root_hub, Driver=uhci_hcd/2p, 12M
 /: Bus 01.Port 1: Dev 1, Class=root_hub, Driver=ehci-pci/8p, 480M
MachineType: Dell Inc. MM061
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-5.8.0-31-generic root=UUID=d590f141-7b8d-421d-84b3-baa43181a241 ro resume=/dev/sda5
SourcePackage: xserver-xorg-input-synaptics
UpgradeStatus: Upgraded to groovy on 2020-10-21 (48 days ago)
dmi.bios.date: 06/13/2007
dmi.bios.release: 1.7
dmi.bios.vendor: Dell Inc.
dmi.bios.version: A17
dmi.board.name: 0XD720
dmi.board.vendor: Dell Inc.
dmi.chassis.type: 8
dmi.chassis.vendor: Dell Inc.
dmi.ec.firmware.release: 1.7
dmi.modalias: dmi:bvnDellInc.:bvrA17:bd06/13/2007:br1.7:efr1.7:svnDellInc.:pnMM061:pvr:rvnDellInc.:rn0XD720:rvr:cvnDellInc.:ct8:cvr:
dmi.product.name: MM061
dmi.sys.vendor: Dell Inc.
version.compiz: compiz N/A
version.libdrm2: libdrm2 2.4.102-1ubuntu1
version.libgl1-mesa-dri: libgl1-mesa-dri 20.2.1-1
version.libgl1-mesa-glx: libgl1-mesa-glx N/A
version.xserver-xorg-core: xserver-xorg-core 2:1.20.9-2ubuntu1.1
version.xserver-xorg-input-evdev: xserver-xorg-input-evdev 1:2.10.6-2
version.xserver-xorg-video-ati: xserver-xorg-video-ati 1:19.1.0-1ubuntu1
version.xserver-xorg-video-intel: xserver-xorg-video-intel N/A
version.xserver-xorg-video-nouveau: xserver-xorg-video-nouveau N/A