device connection to remote device over VLAN not working

I am trying to provide access to a camera on a remote network for a user by configuring VLAN on various L3 HP switches. The network I am working in has numerous VLANs and the path from the device to the camera crosses at least 4 L3 switches. I have been unable to get the connection to work and at this point need troubleshooting tips and a better understanding of how this should work.

At this point I would like to focus on a suggested methodology to troubleshoot connectivity on a VLAN. I have been told ping will not work because this is a L2 VLAN not intended to be routed from everything and that is why ping will not work, I think this is nonsense but please let me know if there is a way to track the VLAN path to see where the disconnect might be. Also, there has to be a L3 component as the source and destination networks are different and the route to the destination is specified on an L3 route table.


The following is the basic configuration:

Device :
Attaches to Switch 1 in VLAN 13 using an untagged (access) port. The PVID (native) VLAN on the configured port is 13.
There is no VLAN 13 interface configured on Switch 1. Using NDP and routing tables, I know that Switch 1 connects to Switch 2 using Tagged (Trunk) ports that include VLAN 13.
Switch 2 does not have an interface configured for VLAN 13.
I am unable to ping the camera from Switch 1 or Switch 2. There are no ARP entries for VLAN 13 in Switch 1. There are VLAN 13 entries in the ARP table on Switch 2. As an experiment, I added a 1301 interface on Switch 2 and I was able to ping the camera at 10.190.100.x  . That same test did not work on Switch 1.
Switch 2 connects to Switch 3 using Tagged (trunk) port.
I am able to ping everything from Switch 3. All three Switches are in different subnets, 10.10.20.x , 10.10.10.x, 10.15.11.x respectively. The camera is in 10.190.100.x .

Here is the real problem. The IP of the camera has a static route assigned on Switch 3 pointing all traffic for 10.190.100.x  to next hop 10.190.190.154  interface VLAN 13. I do not have access to next hop 10.190.190.154 I do not know what that is and I do not fully understand how the VLAN assignment and the route entry work together.

I have been told ping will not work because this is a L2 VLAN not intended to be routed from everything and that is why ping will not work. However, the MAC to IP mapping has to be done somewhere so that the ARP table has that information for the VLAN. I am not sure that any switch I am pinging from will get a return, that is, if 15 VLANS are on a switch should I get a ping response from all of those 15 VLANS?

Any suggestions are appreciated. Clarity on how it should work is key, eg, default gateway vs VLAN port to discover an IP, etc. I am handicapped by the fact that this is a remote network and I do not have hands on site to test quickly so it might take extra time to act on any suggestions.

Thanks,
D