MacBook Pro (13-inch, 2017, Two Thunderbolt 3 ports) running Mojave (10.14.3 (18D42)) is does not recognize external boot drive

I just got a new Macbook Pro, I was previously using an MBP (13-inch, Mid 2012) running Mojave. I have a 1TB SSD that has a partition with a Windows 10 installation (I followed this tutorial: https://blog.macsales.com/40947-tech-tip-how-to-use-boot-camp-on-an-external-drive/) and another MacOS Journaled partition that I use for general file storage. This setup has worked for me on my old MBP (I can hold option to boot into windows). However, the Startup Manager does not recognize my external drive and only display my internal drive. Using System Preferences startup disk leads to this error: The bless tool was unable to set the current boot disk. I've tried resetting NVRAM as well.

Here is some disk information that may help:

$ diskutil list

...

/dev/disk2 (external, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *1.0 TB     disk2
   1:               Windows_NTFS BOOTCAMP                353.1 GB   disk2s1
   2:                  Apple_HFS VECTOTECHS              671.1 GB   disk2s2

$ sudo fdisk /dev/disk2
Disk: /dev/disk2    geometry: 124519/255/63 [2000409264 sectors]
Signature: 0xAA55
         Starting       Ending
 #: id  cyl  hd sec -  cyl  hd sec [     start -       size]
------------------------------------------------------------------------
*1: 07 1023 254  63 - 1023 254  63 [         2 -  689689262] HPFS/QNX/AUX
 2: AF 1023 254  63 - 1023 254  63 [ 689690624 - 1310715904] HFS+
 3: 00    0   0   0 -    0   0   0 [         0 -          0] unused
 4: 00    0   0   0 -    0   0   0 [         0 -          0] unused

My guess is that I need an EFI partition for the newer mac to recognize my drive. Would this entail restarting the entire installation process? Any information would be greatly appreciated :)

Your guess is correct. The 2017 model Macs can only EFI boot Windows. Since the first partition on the external drive starts at sector 2, the drive does not have the space to convert from a MBR partition table scheme to a GUID partition table (GPT) scheme. This means you would need to restart the installation process.

When installing Windows 10, I would recommend you do not use VirtualBox. This recommendation is based on the fact that the Windows 10 ISO from Microsoft and the Windows Support Software from Apple contains all the software required to install Windows 10 to your external drive. Therefore, there is no need to use a third party product such as VirtualBox.

The use of a virtual machine to install Windows dates to when Mac owners removed the optical drive so another HDD or SSD drive could installed in their Mac. After the optical drive was removed, often an owner would discover the Windows 10 installer could not be booted from a flash drive. This led to the use of a virtual machine as the only way to install Windows other than change the hardware configuration.

Since you model Mac can EFI boot from either an internal or external drive, you do not need to use a virtual machine. However, if you wish, a virtual machine can also be used. Below are some references to previously posted methods for installing Windows 10 on an external drive.

Drivers not working on Windows 10 installed (CLI process) on external SSD running on Macbook

Is it possible to use Boot Camp with Windows 10 from an external HDD?

How can I copy the drivers provided by Apple when installing Bootcamp on an external drive?