Thanks @p.colbert, that is both helpful and hilariously obvious in retrospect. If you want to know the time, better look at the clock! 
This works:
from ._anvil_designer import Form1Template
from anvil import *
import time
class Form1(Form1Template):
def __init__(self, **properties):
self.init_components(**properties)
self.start_time = None
self.timer_1.interval = 0.0 # Timer initially inactive
def start_timer(self, **event_args):
print("start_timer pressed")
self.start_time = time.time()
self.timer_1.interval = 0.1 # Start ticking every 0.1 seconds
def timer_1_tick(self, **event_args):
elapsed_seconds = time.time() - self.start_time
self.label_1.text = f"Elapsed time: {elapsed_seconds:.1f} s"