The first three lines of "must haves" on the list below is what is needed at a minimum for this position as the focus for this role is vSAN/SRM and vRealize.  

We have an oncall rotation that is once every six weeks currently.  Page-outs vary based on issues that week and can range from 0 pages to several per week.

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The Virtualization Systems Administrator is an experienced Support Technician with ability to support VMware environments and management of virtual desktop infrastructure and VMware vSphere server Infrastructure with basic design knowledge. Specific job responsibilities include problem and change management, implementing, managing and migrating vSphere/VDI environments using VMware; managing the security and stability of the VMware product(s); managing all facets of the subsystems necessary to support the delivery environment; providing technical project leadership for a vSphere/VDI environment; providing good customer service during all interactions; communicating and working with customers; working as a part of the overall team on a daily basis; following IBM policies and procedures

Must Have experience:
vSAN / VMware Site Recovery Manager (SRM)
vRealize Operations Manager (vROPs/vCOPS)
vSphere 3.x, 4.x and 5.x, 6x to include vCenter Server for Windows, vCenter Server Linux Appliance, VMware ESX and VMware ESXi
IBM/Lenovo System X Hardware
Intel (HP) Server Hardware
VMware PowerCLI
VMware Upgrade experience (4.x to 5.x)
Highly organized and able to meet deadlines
Other Technologies (entry-mid level exp.):
Mid-level Microsoft Windows 2008/2012 experience
Fibre Channel / iSCSI / NFS Technologies