I was able to ultimately find a solution to my issue. Thank you @Kulkul for you assistance. I was able to generate the below code to produce the information I needed.
import clr
clr.AddReference('RevitAPI')
from Autodesk.Revit.DB import *
clr.AddReference("RevitNodes")
import Revit
clr.ImportExtensions(Revit.Elements)
clr.AddReference("RevitServices")
import RevitServices
from RevitServices.Persistence import DocumentManager
from RevitServices.Transactions import TransactionManager
doc = DocumentManager.Instance.CurrentDBDocument
cat = UnwrapElement(IN[0])
subcat = cat.SubCategories
listNames = []
listPattern = []
patname = []
listout = []
listpatid = []
for i in subcat:
name = i.Name
listNames.append(name)
id = i.GetLinePatternId(GraphicsStyleType.Projection)
pat = LinePatternElement.GetLinePattern(doc,id)
listPattern.append(pat)
listpatid.append(id)
try:
patname.append(pat.Name)
except:
patname.append("Solid")
style = i.GetGraphicsStyle(GraphicsStyleType.Projection)
listout.append(style)
OUT = listout, listNames, listPattern, patname, listpatid