Layer-2 switches use MAC address tables, not ARP tables, to determine which MAC addresses were last seen on which switch interfaces. ARP resolves a layer-3 address to a layer-2 address, and a layer-2 switch only cares about that on its management interface, not for switching.
A layer-2 switch will update its MAC address table with the interface on which a MAC address was seen every time a frame enters the switch. The switch looks at the source MAC address and updates its MAC address table with the interface for that source MAC address (the table gets built quickly because it only takes one frame from a MAC address to add/edit a MAC address table entry).
The switch will then look at the destination address, and look that up in the table to determine on which interface the MAC address was last seen as a source address. The switch will then switch the frame to that interface. If the destination MAC address is not in the MAC address table, the switch will flood the frame to all interfaces except the interface where the frame entered the switch.
For example, Cisco Catalyst switches have the:
mac address-table aging-time <seconds> ! old
mac-address-table aging-time <seconds> ! new
depending on the IOS version used on the switch. The default is 300 seconds (5 minutes), and the maximum is 1,000,000 seconds (over 11.5 days).
This must be configured in every switch so that the switch MAC address table doesn't time out.
ARP is broadcast by the hosts in order to resolve the layer-2 destination MAC address from the layer-3 destination IPv4 address. The hosts maintain ARP tables, and ARP requests are broadcast to all other hosts, so ARP requests (and gratuitous ARP) will be broadcast to all switch interfaces on the broadcast domain (VLAN). Depending on the host OS, you can probably configure the ARP table timeout, but host configurations are off-topic here.
Some switches can reduce unknown unicast flooding, or send unknown unicasts to a particular interface. This can cause problems if not used correctly, so be careful if your switches support this.